A Morse Bott Approach To Monopole Floer Homology And The Triangulation Conjecture

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A Morse-Bott Approach to Monopole Floer Homology and the Triangulation Conjecture

Francesco Lin
A Morse Bott Approach to Monopole Floer Homology and the Triangulation Conjecture Book PDF

Author : Francesco Lin
Publisher : American Mathematical Soc.
Page : 162 pages
File Size : 41,5 Mb
Release : 2018-10-03
Category : Floer homology
ISBN : 9781470429638

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A Morse-Bott Approach to Monopole Floer Homology and the Triangulation Conjecture by Francesco Lin Pdf

In the present work the author generalizes the construction of monopole Floer homology due to Kronheimer and Mrowka to the case of a gradient flow with Morse-Bott singularities. Focusing then on the special case of a three-manifold equipped equipped with a structure which is isomorphic to its conjugate, the author defines the counterpart in this context of Manolescu's recent Pin(2)-equivariant Seiberg-Witten-Floer homology. In particular, the author provides an alternative approach to his disproof of the celebrated Triangulation conjecture.

Breadth in Contemporary Topology

David T. Gay,Weiwei Wu
Breadth in Contemporary Topology Book PDF

Author : David T. Gay,Weiwei Wu
Publisher : American Mathematical Soc.
Page : 282 pages
File Size : 50,7 Mb
Release : 2019-06-27
Category : Algebraic topology -- Homotopy theory -- Loop space machines, operads
ISBN : 9781470442491

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Breadth in Contemporary Topology by David T. Gay,Weiwei Wu Pdf

This volume contains the proceedings of the 2017 Georgia International Topology Conference, held from May 22–June 2, 2017, at the University of Georgia, Athens, Georgia. The papers contained in this volume cover topics ranging from symplectic topology to classical knot theory to topology of 3- and 4-dimensional manifolds to geometric group theory. Several papers focus on open problems, while other papers present new and insightful proofs of classical results. Taken as a whole, this volume captures the spirit of the conference, both in terms of public lectures and informal conversations, and presents a sampling of some of the great new ideas generated in topology over the preceding eight years.

An SO(3)-Monopole Cobordism Formula Relating Donaldson and Seiberg-Witten Invariants

Paul Feehan,Thomas G. Leness
An SO 3 Monopole Cobordism Formula Relating Donaldson and Seiberg Witten Invariants Book PDF

Author : Paul Feehan,Thomas G. Leness
Publisher : American Mathematical Soc.
Page : 228 pages
File Size : 55,7 Mb
Release : 2019-01-08
Category : Cobordism theory
ISBN : 9781470414214

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An SO(3)-Monopole Cobordism Formula Relating Donaldson and Seiberg-Witten Invariants by Paul Feehan,Thomas G. Leness Pdf

The authors prove an analogue of the Kotschick–Morgan Conjecture in the context of monopoles, obtaining a formula relating the Donaldson and Seiberg–Witten invariants of smooth four-manifolds using the -monopole cobordism. The main technical difficulty in the -monopole program relating the Seiberg–Witten and Donaldson invariants has been to compute intersection pairings on links of strata of reducible monopoles, namely the moduli spaces of Seiberg–Witten monopoles lying in lower-level strata of the Uhlenbeck compactification of the moduli space of monopoles. In this monograph, the authors prove—modulo a gluing theorem which is an extension of their earlier work—that these intersection pairings can be expressed in terms of topological data and Seiberg–Witten invariants of the four-manifold. Their proofs that the -monopole cobordism yields both the Superconformal Simple Type Conjecture of Moore, Mariño, and Peradze and Witten's Conjecture in full generality for all closed, oriented, smooth four-manifolds with and odd appear in earlier works.

Automorphisms ofTwo-Generator Free Groups and Spaces of Isometric Actions on the Hyperbolic Plane

William Goldman,Greg McShane,George Stantchev,Ser Peow Tan
Automorphisms ofTwo Generator Free Groups and Spaces of Isometric Actions on the Hyperbolic Plane Book PDF

Author : William Goldman,Greg McShane,George Stantchev,Ser Peow Tan
Publisher : American Mathematical Soc.
Page : 78 pages
File Size : 55,7 Mb
Release : 2019-06-10
Category : Automorphisms
ISBN : 9781470436148

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Automorphisms ofTwo-Generator Free Groups and Spaces of Isometric Actions on the Hyperbolic Plane by William Goldman,Greg McShane,George Stantchev,Ser Peow Tan Pdf

The automorphisms of a two-generator free group F acting on the space of orientation-preserving isometric actions of F on hyperbolic 3-space defines a dynamical system. Those actions which preserve a hyperbolic plane but not an orientation on that plane is an invariant subsystem, which reduces to an action of a group on by polynomial automorphisms preserving the cubic polynomial and an area form on the level surfaces .

Fusion of Defects

Arthur Bartels,Christopher Douglas,André Henriques
Fusion of Defects Book PDF

Author : Arthur Bartels,Christopher Douglas,André Henriques
Publisher : American Mathematical Soc.
Page : 102 pages
File Size : 47,8 Mb
Release : 2019-04-10
Category : Generalized spaces
ISBN : 9781470435233

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Fusion of Defects by Arthur Bartels,Christopher Douglas,André Henriques Pdf

Conformal nets provide a mathematical model for conformal field theory. The authors define a notion of defect between conformal nets, formalizing the idea of an interaction between two conformal field theories. They introduce an operation of fusion of defects, and prove that the fusion of two defects is again a defect, provided the fusion occurs over a conformal net of finite index. There is a notion of sector (or bimodule) between two defects, and operations of horizontal and vertical fusion of such sectors. The authors' most difficult technical result is that the horizontal fusion of the vacuum sectors of two defects is isomorphic to the vacuum sector of the fused defect. Equipped with this isomorphism, they construct the basic interchange isomorphism between the horizontal fusion of two vertical fusions and the vertical fusion of two horizontal fusions of sectors.

Geometric Pressure for Multimodal Maps of the Interval

Feliks Przytycki,Juan Rivera-Letelier
Geometric Pressure for Multimodal Maps of the Interval Book PDF

Author : Feliks Przytycki,Juan Rivera-Letelier
Publisher : American Mathematical Soc.
Page : 81 pages
File Size : 40,7 Mb
Release : 2019-06-10
Category : Conformal geometry
ISBN : 9781470435677

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Geometric Pressure for Multimodal Maps of the Interval by Feliks Przytycki,Juan Rivera-Letelier Pdf

This paper is an interval dynamics counterpart of three theories founded earlier by the authors, S. Smirnov and others in the setting of the iteration of rational maps on the Riemann sphere: the equivalence of several notions of non-uniform hyperbolicity, Geometric Pressure, and Nice Inducing Schemes methods leading to results in thermodynamical formalism. The authors work in a setting of generalized multimodal maps, that is, smooth maps f of a finite union of compact intervals Iˆ in R into R with non-flat critical points, such that on its maximal forward invariant set K the map f is topologically transitive and has positive topological entropy. They prove that several notions of non-uniform hyperbolicity of f|K are equivalent (including uniform hyperbolicity on periodic orbits, TCE & all periodic orbits in K hyperbolic repelling, Lyapunov hyperbolicity, and exponential shrinking of pull-backs). They prove that several definitions of geometric pressure P(t), that is pressure for the map f|K and the potential −tlog|f′|, give the same value (including pressure on periodic orbits, “tree” pressure, variational pressures and conformal pressure). Finally they prove that, provided all periodic orbits in K are hyperbolic repelling, the function P(t) is real analytic for t between the “condensation” and “freezing” parameters and that for each such t there exists unique equilibrium (and conformal) measure satisfying strong statistical properties.

Quiver Grassmannians of Extended Dynkin Type D Part I: Schubert Systems and Decompositions into Affine Spaces

Oliver Lorscheid,Thorsten Weist
Quiver Grassmannians of Extended Dynkin Type D Part I Schubert Systems and Decompositions into Affine Spaces Book PDF

Author : Oliver Lorscheid,Thorsten Weist
Publisher : American Mathematical Soc.
Page : 78 pages
File Size : 48,6 Mb
Release : 2019-12-02
Category : Education
ISBN : 9781470436476

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Quiver Grassmannians of Extended Dynkin Type D Part I: Schubert Systems and Decompositions into Affine Spaces by Oliver Lorscheid,Thorsten Weist Pdf

Let Q be a quiver of extended Dynkin type D˜n. In this first of two papers, the authors show that the quiver Grassmannian Gre–(M) has a decomposition into affine spaces for every dimension vector e– and every indecomposable representation M of defect −1 and defect 0, with the exception of the non-Schurian representations in homogeneous tubes. The authors characterize the affine spaces in terms of the combinatorics of a fixed coefficient quiver for M. The method of proof is to exhibit explicit equations for the Schubert cells of Gre–(M) and to solve this system of equations successively in linear terms. This leads to an intricate combinatorial problem, for whose solution the authors develop the theory of Schubert systems. In Part 2 of this pair of papers, they extend the result of this paper to all indecomposable representations M of Q and determine explicit formulae for the F-polynomial of M.

Crossed Products of Operator Algebras

Elias G. Katsoulis,Christopher Ramsey
Crossed Products of Operator Algebras Book PDF

Author : Elias G. Katsoulis,Christopher Ramsey
Publisher : American Mathematical Soc.
Page : 85 pages
File Size : 40,7 Mb
Release : 2019-04-10
Category : C*-algebras
ISBN : 9781470435455

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Crossed Products of Operator Algebras by Elias G. Katsoulis,Christopher Ramsey Pdf

The authors study crossed products of arbitrary operator algebras by locally compact groups of completely isometric automorphisms. They develop an abstract theory that allows for generalizations of many of the fundamental results from the selfadjoint theory to our context. They complement their generic results with the detailed study of many important special cases. In particular they study crossed products of tensor algebras, triangular AF algebras and various associated C -algebras. They make contributions to the study of C -envelopes, semisimplicity, the semi-Dirichlet property, Takai duality and the Hao-Ng isomorphism problem. They also answer questions from the pertinent literature.

Time Changes of the Brownian Motion: Poincaré Inequality, Heat Kernel Estimate and Protodistance

Jun Kigami
Time Changes of the Brownian Motion Poincar Inequality Heat Kernel Estimate and Protodistance Book PDF

Author : Jun Kigami
Publisher : American Mathematical Soc.
Page : 118 pages
File Size : 41,6 Mb
Release : 2019-06-10
Category : Brownian motion processes
ISBN : 9781470436209

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Time Changes of the Brownian Motion: Poincaré Inequality, Heat Kernel Estimate and Protodistance by Jun Kigami Pdf

In this paper, time changes of the Brownian motions on generalized Sierpinski carpets including n-dimensional cube [0,1]n are studied. Intuitively time change corresponds to alteration to density of the medium where the heat flows. In case of the Brownian motion on [0,1]n, density of the medium is homogeneous and represented by the Lebesgue measure. The author's study includes densities which are singular to the homogeneous one. He establishes a rich class of measures called measures having weak exponential decay. This class contains measures which are singular to the homogeneous one such as Liouville measures on [0,1]2 and self-similar measures. The author shows the existence of time changed process and associated jointly continuous heat kernel for this class of measures. Furthermore, he obtains diagonal lower and upper estimates of the heat kernel as time tends to 0. In particular, to express the principal part of the lower diagonal heat kernel estimate, he introduces “protodistance” associated with the density as a substitute of ordinary metric. If the density has the volume doubling property with respect to the Euclidean metric, the protodistance is shown to produce metrics under which upper off-diagonal sub-Gaussian heat kernel estimate and lower near diagonal heat kernel estimate will be shown.

Flat Rank Two Vector Bundles on Genus Two Curves

Viktoria Heu,Frank Loray
Flat Rank Two Vector Bundles on Genus Two Curves Book PDF

Author : Viktoria Heu,Frank Loray
Publisher : American Mathematical Soc.
Page : 103 pages
File Size : 41,6 Mb
Release : 2019-06-10
Category : Electronic
ISBN : 9781470435660

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Flat Rank Two Vector Bundles on Genus Two Curves by Viktoria Heu,Frank Loray Pdf

The authors study the moduli space of trace-free irreducible rank 2 connections over a curve of genus 2 and the forgetful map towards the moduli space of underlying vector bundles (including unstable bundles), for which they compute a natural Lagrangian rational section. As a particularity of the genus case, connections as above are invariant under the hyperelliptic involution: they descend as rank logarithmic connections over the Riemann sphere. The authors establish explicit links between the well-known moduli space of the underlying parabolic bundles with the classical approaches by Narasimhan-Ramanan, Tyurin and Bertram. This allows the authors to explain a certain number of geometric phenomena in the considered moduli spaces such as the classical -configuration of the Kummer surface. The authors also recover a Poincaré family due to Bolognesi on a degree 2 cover of the Narasimhan-Ramanan moduli space. They explicitly compute the Hitchin integrable system on the moduli space of Higgs bundles and compare the Hitchin Hamiltonians with those found by van Geemen-Previato. They explicitly describe the isomonodromic foliation in the moduli space of vector bundles with -connection over curves of genus 2 and prove the transversality of the induced flow with the locus of unstable bundles.

One-Dimensional Empirical Measures, Order Statistics, and Kantorovich Transport Distances

Sergey Bobkov,Michel Ledoux
One Dimensional Empirical Measures Order Statistics and Kantorovich Transport Distances Book PDF

Author : Sergey Bobkov,Michel Ledoux
Publisher : American Mathematical Soc.
Page : 126 pages
File Size : 42,5 Mb
Release : 2019-12-02
Category : Education
ISBN : 9781470436506

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One-Dimensional Empirical Measures, Order Statistics, and Kantorovich Transport Distances by Sergey Bobkov,Michel Ledoux Pdf

This work is devoted to the study of rates of convergence of the empirical measures μn=1n∑nk=1δXk, n≥1, over a sample (Xk)k≥1 of independent identically distributed real-valued random variables towards the common distribution μ in Kantorovich transport distances Wp. The focus is on finite range bounds on the expected Kantorovich distances E(Wp(μn,μ)) or [E(Wpp(μn,μ))]1/p in terms of moments and analytic conditions on the measure μ and its distribution function. The study describes a variety of rates, from the standard one 1n√ to slower rates, and both lower and upper-bounds on E(Wp(μn,μ)) for fixed n in various instances. Order statistics, reduction to uniform samples and analysis of beta distributions, inverse distribution functions, log-concavity are main tools in the investigation. Two detailed appendices collect classical and some new facts on inverse distribution functions and beta distributions and their densities necessary to the investigation.

Moufang Sets and Structurable Division Algebras

Lien Boelaert,Tom De Medts,Anastasia Stavrova
Moufang Sets and Structurable Division Algebras Book PDF

Author : Lien Boelaert,Tom De Medts,Anastasia Stavrova
Publisher : American Mathematical Soc.
Page : 90 pages
File Size : 47,9 Mb
Release : 2019-06-10
Category : Combinatorial group theory
ISBN : 9781470435547

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Moufang Sets and Structurable Division Algebras by Lien Boelaert,Tom De Medts,Anastasia Stavrova Pdf

A Moufang set is essentially a doubly transitive permutation group such that each point stabilizer contains a normal subgroup which is regular on the remaining vertices; these regular normal subgroups are called the root groups, and they are assumed to be conjugate and to generate the whole group. It has been known for some time that every Jordan division algebra gives rise to a Moufang set with abelian root groups. The authors extend this result by showing that every structurable division algebra gives rise to a Moufang set, and conversely, they show that every Moufang set arising from a simple linear algebraic group of relative rank one over an arbitrary field k of characteristic different from 2 and 3 arises from a structurable division algebra. The authors also obtain explicit formulas for the root groups, the τ-map and the Hua maps of these Moufang sets. This is particularly useful for the Moufang sets arising from exceptional linear algebraic groups.

Generalized Mercer Kernels and Reproducing Kernel Banach Spaces

Yuesheng Xu,Qi Ye
Generalized Mercer Kernels and Reproducing Kernel Banach Spaces Book PDF

Author : Yuesheng Xu,Qi Ye
Publisher : American Mathematical Soc.
Page : 122 pages
File Size : 48,7 Mb
Release : 2019-04-10
Category : Banach spaces
ISBN : 9781470435509

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Generalized Mercer Kernels and Reproducing Kernel Banach Spaces by Yuesheng Xu,Qi Ye Pdf

This article studies constructions of reproducing kernel Banach spaces (RKBSs) which may be viewed as a generalization of reproducing kernel Hilbert spaces (RKHSs). A key point is to endow Banach spaces with reproducing kernels such that machine learning in RKBSs can be well-posed and of easy implementation. First the authors verify many advanced properties of the general RKBSs such as density, continuity, separability, implicit representation, imbedding, compactness, representer theorem for learning methods, oracle inequality, and universal approximation. Then, they develop a new concept of generalized Mercer kernels to construct p-norm RKBSs for 1≤p≤∞ .

Spinors on Singular Spaces and the Topology of Causal Fermion Systems

Felix Finster,Niky Kamran
Spinors on Singular Spaces and the Topology of Causal Fermion Systems Book PDF

Author : Felix Finster,Niky Kamran
Publisher : American Mathematical Soc.
Page : 83 pages
File Size : 41,9 Mb
Release : 2019-06-10
Category : Electronic
ISBN : 9781470436216

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Spinors on Singular Spaces and the Topology of Causal Fermion Systems by Felix Finster,Niky Kamran Pdf

Causal fermion systems and Riemannian fermion systems are proposed as a framework for describing non-smooth geometries. In particular, this framework provides a setting for spinors on singular spaces. The underlying topological structures are introduced and analyzed. The connection to the spin condition in differential topology is worked out. The constructions are illustrated by many simple examples such as the Euclidean plane, the two-dimensional Minkowski space, a conical singularity, a lattice system as well as the curvature singularity of the Schwarzschild space-time. As further examples, it is shown how complex and Kähler structures can be encoded in Riemannian fermion systems.

CR Embedded Submanifolds of CR Manifolds

Sean N. Curry,A. Rod Gover
CR Embedded Submanifolds of CR Manifolds Book PDF

Author : Sean N. Curry,A. Rod Gover
Publisher : American Mathematical Soc.
Page : 81 pages
File Size : 55,9 Mb
Release : 2019-04-10
Category : CR submanifolds
ISBN : 9781470435448

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CR Embedded Submanifolds of CR Manifolds by Sean N. Curry,A. Rod Gover Pdf

The authors develop a complete local theory for CR embedded submanifolds of CR manifolds in a way which parallels the Ricci calculus for Riemannian submanifold theory. They define a normal tractor bundle in the ambient standard tractor bundle along the submanifold and show that the orthogonal complement of this bundle is not canonically isomorphic to the standard tractor bundle of the submanifold. By determining the subtle relationship between submanifold and ambient CR density bundles the authors are able to invariantly relate these two tractor bundles, and hence to invariantly relate the normal Cartan connections of the submanifold and ambient manifold by a tractor analogue of the Gauss formula. This also leads to CR analogues of the Gauss, Codazzi, and Ricci equations. The tractor Gauss formula includes two basic invariants of a CR embedding which, along with the submanifold and ambient curvatures, capture the jet data of the structure of a CR embedding. These objects therefore form the basic building blocks for the construction of local invariants of the embedding. From this basis the authors develop a broad calculus for the construction of the invariants and invariant differential operators of CR embedded submanifolds. The CR invariant tractor calculus of CR embeddings is developed concretely in terms of the Tanaka-Webster calculus of an arbitrary (suitably adapted) ambient contact form. This enables straightforward and explicit calculation of the pseudohermitian invariants of the embedding which are also CR invariant. These are extremely difficult to find and compute by more naïve methods. The authors conclude by establishing a CR analogue of the classical Bonnet theorem in Riemannian submanifold theory.