Quasi Actions On Trees Ii Finite Depth Bass Serre Trees

Quasi Actions On Trees Ii Finite Depth Bass Serre Trees Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Quasi Actions On Trees Ii Finite Depth Bass Serre Trees book. This book definitely worth reading, it is an incredibly well-written.

Quasi-Actions on Trees II: Finite Depth Bass-Serre Trees

Lee Mosher,Michah Sageev,Kevin Whyte
Quasi Actions on Trees II Finite Depth Bass Serre Trees Book PDF

Author : Lee Mosher,Michah Sageev,Kevin Whyte
Publisher : American Mathematical Soc.
Page : 118 pages
File Size : 46,5 Mb
Release : 2011
Category : Geometric group theory
ISBN : 9780821847121

Get Book

Quasi-Actions on Trees II: Finite Depth Bass-Serre Trees by Lee Mosher,Michah Sageev,Kevin Whyte Pdf

This paper addresses questions of quasi-isometric rigidity and classification for fundamental groups of finite graphs of groups, under the assumption that the Bass-Serre tree of the graph of groups has finite depth. The main example of a finite depth graph of groups is one whose vertex and edge groups are coarse Poincare duality groups. The main theorem says that, under certain hypotheses, if $\mathcal{G}$ is a finite graph of coarse Poincare duality groups, then any finitely generated group quasi-isometric to the fundamental group of $\mathcal{G}$ is also the fundamental group of a finite graph of coarse Poincare duality groups, and any quasi-isometry between two such groups must coarsely preserve the vertex and edge spaces of their Bass-Serre trees of spaces. Besides some simple normalization hypotheses, the main hypothesis is the ``crossing graph condition'', which is imposed on each vertex group $\mathcal{G}_v$ which is an $n$-dimensional coarse Poincare duality group for which every incident edge group has positive codimension: the crossing graph of $\mathcal{G}_v$ is a graph $\epsilon_v$ that describes the pattern in which the codimension 1 edge groups incident to $\mathcal{G}_v$ are crossed by other edge groups incident to $\mathcal{G}_v$, and the crossing graph condition requires that $\epsilon_v$ be connected or empty.

Quasi-actions on Trees II

Lee Mosher,Michah Sageev,Kevin Whyte
Quasi actions on Trees II Book PDF

Author : Lee Mosher,Michah Sageev,Kevin Whyte
Publisher : American Mathematical Soc.
Page : 118 pages
File Size : 49,9 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 9780821882535

Get Book

Quasi-actions on Trees II by Lee Mosher,Michah Sageev,Kevin Whyte Pdf

"November 2011, volume 214, number 1008 (fourth of 5 numbers)."

New Directions in Locally Compact Groups

Pierre-Emmanuel Caprace,Nicolas Monod
New Directions in Locally Compact Groups Book PDF

Author : Pierre-Emmanuel Caprace,Nicolas Monod
Publisher : Cambridge University Press
Page : 367 pages
File Size : 42,7 Mb
Release : 2018-02-08
Category : Mathematics
ISBN : 9781108413121

Get Book

New Directions in Locally Compact Groups by Pierre-Emmanuel Caprace,Nicolas Monod Pdf

A snapshot of the major renaissance happening today in the study of locally compact groups and their many applications.

Geometric Group Theory

Cornelia Druţu,Michael Kapovich
Geometric Group Theory Book PDF

Author : Cornelia Druţu,Michael Kapovich
Publisher : American Mathematical Soc.
Page : 819 pages
File Size : 43,6 Mb
Release : 2018-03-28
Category : Geometric group theory
ISBN : 9781470411046

Get Book

Geometric Group Theory by Cornelia Druţu,Michael Kapovich Pdf

The key idea in geometric group theory is to study infinite groups by endowing them with a metric and treating them as geometric spaces. This applies to many groups naturally appearing in topology, geometry, and algebra, such as fundamental groups of manifolds, groups of matrices with integer coefficients, etc. The primary focus of this book is to cover the foundations of geometric group theory, including coarse topology, ultralimits and asymptotic cones, hyperbolic groups, isoperimetric inequalities, growth of groups, amenability, Kazhdan's Property (T) and the Haagerup property, as well as their characterizations in terms of group actions on median spaces and spaces with walls. The book contains proofs of several fundamental results of geometric group theory, such as Gromov's theorem on groups of polynomial growth, Tits's alternative, Stallings's theorem on ends of groups, Dunwoody's accessibility theorem, the Mostow Rigidity Theorem, and quasiisometric rigidity theorems of Tukia and Schwartz. This is the first book in which geometric group theory is presented in a form accessible to advanced graduate students and young research mathematicians. It fills a big gap in the literature and will be used by researchers in geometric group theory and its applications.

Finite Order Automorphisms and Real Forms of Affine Kac-Moody Algebras in the Smooth and Algebraic Category

Ernst Heintze,Christian Gross
Finite Order Automorphisms and Real Forms of Affine Kac Moody Algebras in the Smooth and Algebraic Category Book PDF

Author : Ernst Heintze,Christian Gross
Publisher : American Mathematical Soc.
Page : 66 pages
File Size : 48,9 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821869185

Get Book

Finite Order Automorphisms and Real Forms of Affine Kac-Moody Algebras in the Smooth and Algebraic Category by Ernst Heintze,Christian Gross Pdf

Let $\mathfrak{g}$ be a real or complex (finite dimensional) simple Lie algebra and $\sigma\in\mathrm{Aut}\mathfrak{g}$. The authors study automorphisms of the twisted loop algebra $L(\mathfrak{g},\sigma)$ of smooth $\sigma$-periodic maps from $\mathbb{R}$ to $\mathfrak{g}$ as well as of the ``smooth'' affine Kac-Moody algebra $\hat L(\mathfrak{g},\sigma)$, which is a $2$-dimensional extension of $L(\mathfrak{g},\sigma)$. It turns out that these automorphisms which either preserve or reverse the orientation of loops, and are correspondingly called to be of first and second kind, can be described essentially by curves of automorphisms of $\mathfrak{g}$. If the order of the automorphisms is finite, then the corresponding curves in $\mathrm{Aut}\mathfrak{g}$ allow us to define certain invariants and these turn out to parametrize the conjugacy classes of the automorphisms. If their order is $2$ the authors carry this out in detail and deduce a complete classification of involutions and real forms (which correspond to conjugate linear involutions) of smooth affine Kac-Moody algebras.

The resulting classification can be seen as an extension of Cartan's classification of symmetric spaces, i.e. of involutions on $\mathfrak{g}$. If $\mathfrak{g}$ is compact, then conjugate linear extensions of involutions from $\hat L(\mathfrak{g},\sigma)$ to conjugate linear involutions on $\hat L(\mathfrak{g}_{\mathbb{C}},\sigma_{\mathbb{C}})$ yield a bijection between their conjugacy classes and this gives existence and uniqueness of Cartan decompositions of real forms of complex smooth affine Kac-Moody algebras.

The authors show that their methods work equally well also in the algebraic case where the loops are assumed to have finite Fourier expansions.

The Hermitian Two Matrix Model with an Even Quartic Potential

Maurice Duits,Arno B. J. Kuijlaars,Man Yue Mo
The Hermitian Two Matrix Model with an Even Quartic Potential Book PDF

Author : Maurice Duits,Arno B. J. Kuijlaars,Man Yue Mo
Publisher : American Mathematical Soc.
Page : 105 pages
File Size : 48,7 Mb
Release : 2012
Category : Boundary value problems
ISBN : 9780821869284

Get Book

The Hermitian Two Matrix Model with an Even Quartic Potential by Maurice Duits,Arno B. J. Kuijlaars,Man Yue Mo Pdf

The authors consider the two matrix model with an even quartic potential $W(y)=y^4/4+\alpha y^2/2$ and an even polynomial potential $V(x)$. The main result of the paper is the formulation of a vector equilibrium problem for the limiting mean density for the eigenvalues of one of the matrices $M_1$. The vector equilibrium problem is defined for three measures, with external fields on the first and third measures and an upper constraint on the second measure. The proof is based on a steepest descent analysis of a $4\times4$ matrix valued Riemann-Hilbert problem that characterizes the correlation kernel for the eigenvalues of $M_1$. The authors' results generalize earlier results for the case $\alpha=0$, where the external field on the third measure was not present.

Hopf Algebras and Congruence Subgroups

Yorck Sommerhäuser,Yongchang Zhu
Hopf Algebras and Congruence Subgroups Book PDF

Author : Yorck Sommerhäuser,Yongchang Zhu
Publisher : American Mathematical Soc.
Page : 134 pages
File Size : 53,5 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821869130

Get Book

Hopf Algebras and Congruence Subgroups by Yorck Sommerhäuser,Yongchang Zhu Pdf

The authors prove that the kernel of the action of the modular group on the center of a semisimple factorizable Hopf algebra is a congruence subgroup whenever this action is linear. If the action is only projective, they show that the projective kernel is a congruence subgroup. To do this, they introduce a class of generalized Frobenius-Schur indicators and endow it with an action of the modular group that is compatible with the original one.

Vector Bundles on Degenerations of Elliptic Curves and Yang-Baxter Equations

Igor Burban,Bernd Kreussler
Vector Bundles on Degenerations of Elliptic Curves and Yang Baxter Equations Book PDF

Author : Igor Burban,Bernd Kreussler
Publisher : American Mathematical Soc.
Page : 131 pages
File Size : 52,6 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821872925

Get Book

Vector Bundles on Degenerations of Elliptic Curves and Yang-Baxter Equations by Igor Burban,Bernd Kreussler Pdf

"November 2012, volume 220, number 1035 (third of 4 numbers)."

Elliptic Integrable Systems

Idrisse Khemar
Elliptic Integrable Systems Book PDF

Author : Idrisse Khemar
Publisher : American Mathematical Soc.
Page : 217 pages
File Size : 44,7 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821869253

Get Book

Elliptic Integrable Systems by Idrisse Khemar Pdf

In this paper, the author studies all the elliptic integrable systems, in the sense of C, that is to say, the family of all the $m$-th elliptic integrable systems associated to a $k^\prime$-symmetric space $N=G/G_0$. The author describes the geometry behind this family of integrable systems for which we know how to construct (at least locally) all the solutions. The introduction gives an overview of all the main results, as well as some related subjects and works, and some additional motivations.

Modular Branching Rules for Projective Representations of Symmetric Groups and Lowering Operators for the Supergroup $Q(n)$

Aleksandr Sergeevich Kleshchëv,Vladimir Shchigolev
Modular Branching Rules for Projective Representations of Symmetric Groups and Lowering Operators for the Supergroup Q n Book PDF

Author : Aleksandr Sergeevich Kleshchëv,Vladimir Shchigolev
Publisher : American Mathematical Soc.
Page : 123 pages
File Size : 48,9 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821874318

Get Book

Modular Branching Rules for Projective Representations of Symmetric Groups and Lowering Operators for the Supergroup $Q(n)$ by Aleksandr Sergeevich Kleshchëv,Vladimir Shchigolev Pdf

There are two approaches to projective representation theory of symmetric and alternating groups, which are powerful enough to work for modular representations. One is based on Sergeev duality, which connects projective representation theory of the symmetric group and representation theory of the algebraic supergroup $Q(n)$ via appropriate Schur (super)algebras and Schur functors. The second approach follows the work of Grojnowski for classical affine and cyclotomic Hecke algebras and connects projective representation theory of symmetric groups in characteristic $p$ to the crystal graph of the basic module of the twisted affine Kac-Moody algebra of type $A_{p-1}^{(2)}$. The goal of this work is to connect the two approaches mentioned above and to obtain new branching results for projective representations of symmetric groups.

Infinite-dimensional Representations of 2-groups

John C. Baez
Infinite dimensional Representations of 2 groups Book PDF

Author : John C. Baez
Publisher : American Mathematical Soc.
Page : 120 pages
File Size : 53,5 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821872840

Get Book

Infinite-dimensional Representations of 2-groups by John C. Baez Pdf

A “$2$-group'' is a category equipped with a multiplication satisfying laws like those of a group. Just as groups have representations on vector spaces, $2$-groups have representations on “$2$-vector spaces'', which are categories analogous to vector spaces. Unfortunately, Lie $2$-groups typically have few representations on the finite-dimensional $2$-vector spaces introduced by Kapranov and Voevodsky. For this reason, Crane, Sheppeard and Yetter introduced certain infinite-dimensional $2$-vector spaces called ``measurable categories'' (since they are closely related to measurable fields of Hilbert spaces), and used these to study infinite-dimensional representations of certain Lie $2$-groups. Here they continue this work.

They begin with a detailed study of measurable categories. Then they give a geometrical description of the measurable representations, intertwiners and $2$-intertwiners for any skeletal measurable $2$-group. They study tensor products and direct sums for representations, and various concepts of subrepresentation. They describe direct sums of intertwiners, and sub-intertwiners--features not seen in ordinary group representation theory and study irreducible and indecomposable representations and intertwiners. They also study “irretractable'' representations--another feature not seen in ordinary group representation theory. Finally, they argue that measurable categories equipped with some extra structure deserve to be considered “separable $2$-Hilbert spaces'', and compare this idea to a tentative definition of $2$-Hilbert spaces as representation categories of commutative von Neumann algebras.

Extended Graphical Calculus for Categorified Quantum Sl(2)

Mikhail Khovanov
Extended Graphical Calculus for Categorified Quantum Sl 2 Book PDF

Author : Mikhail Khovanov
Publisher : American Mathematical Soc.
Page : 87 pages
File Size : 49,9 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821889770

Get Book

Extended Graphical Calculus for Categorified Quantum Sl(2) by Mikhail Khovanov Pdf

A categorification of the Beilinson-Lusztig-MacPherson form of the quantum sl(2) was constructed in a paper (arXiv:0803.3652) by Aaron D. Lauda. Here the authors enhance the graphical calculus introduced and developed in that paper to include two-morphisms between divided powers one-morphisms and their compositions. They obtain explicit diagrammatical formulas for the decomposition of products of divided powers one-morphisms as direct sums of indecomposable one-morphisms; the latter are in a bijection with the Lusztig canonical basis elements.

These formulas have integral coefficients and imply that one of the main results of Lauda's paper--identification of the Grothendieck ring of his 2-category with the idempotented quantum sl(2)--also holds when the 2-category is defined over the ring of integers rather than over a field. A new diagrammatic description of Schur functions is also given and it is shown that the the Jacobi-Trudy formulas for the decomposition of Schur functions into elementary or complete symmetric functions follows from the diagrammatic relations for categorified quantum sl(2).

A Theory of Generalized Donaldson-Thomas Invariants

Dominic D. Joyce,Yinan Song
A Theory of Generalized Donaldson Thomas Invariants Book PDF

Author : Dominic D. Joyce,Yinan Song
Publisher : American Mathematical Soc.
Page : 199 pages
File Size : 50,9 Mb
Release : 2012
Category : Calabi-Yau manifolds
ISBN : 9780821852798

Get Book

A Theory of Generalized Donaldson-Thomas Invariants by Dominic D. Joyce,Yinan Song Pdf

This book studies generalized Donaldson-Thomas invariants $\bar{DT}{}^\alpha(\tau)$. They are rational numbers which `count' both $\tau$-stable and $\tau$-semistable coherent sheaves with Chern character $\alpha$ on $X$; strictly $\tau$-semistable sheaves must be counted with complicated rational weights. The $\bar{DT}{}^\alpha(\tau)$ are defined for all classes $\alpha$, and are equal to $DT^\alpha(\tau)$ when it is defined. They are unchanged under deformations of $X$, and transform by a wall-crossing formula under change of stability condition $\tau$. To prove all this, the authors study the local structure of the moduli stack $\mathfrak M$ of coherent sheaves on $X$. They show that an atlas for $\mathfrak M$ may be written locally as $\mathrm{Crit}(f)$ for $f:U\to{\mathbb C}$ holomorphic and $U$ smooth, and use this to deduce identities on the Behrend function $\nu_\mathfrak M$. They compute the invariants $\bar{DT}{}^\alpha(\tau)$ in examples, and make a conjecture about their integrality properties. They also extend the theory to abelian categories $\mathrm{mod}$-$\mathbb{C}Q\backslash I$ of representations of a quiver $Q$ with relations $I$ coming from a superpotential $W$ on $Q$.

On First and Second Order Planar Elliptic Equations with Degeneracies

Abdelhamid Meziani
On First and Second Order Planar Elliptic Equations with Degeneracies Book PDF

Author : Abdelhamid Meziani
Publisher : American Mathematical Soc.
Page : 77 pages
File Size : 54,8 Mb
Release : 2012
Category : Degenerate differential equations
ISBN : 9780821853122

Get Book

On First and Second Order Planar Elliptic Equations with Degeneracies by Abdelhamid Meziani Pdf

This paper deals with elliptic equations in the plane with degeneracies. The equations are generated by a complex vector field that is elliptic everywhere except along a simple closed curve. Kernels for these equations are constructed. Properties of solutions, in a neighborhood of the degeneracy curve, are obtained through integral and series representations. An application to a second order elliptic equation with a punctual singularity is given.

Networking Seifert Surgeries on Knots

Arnaud Deruelle,Katura Miyazaki,Kimihiko Motegi
Networking Seifert Surgeries on Knots Book PDF

Author : Arnaud Deruelle,Katura Miyazaki,Kimihiko Motegi
Publisher : American Mathematical Soc.
Page : 130 pages
File Size : 41,7 Mb
Release : 2012
Category : Complex manifolds
ISBN : 9780821853337

Get Book

Networking Seifert Surgeries on Knots by Arnaud Deruelle,Katura Miyazaki,Kimihiko Motegi Pdf

The authors propose a new approach in studying Dehn surgeries on knots in the $3$-sphere $S^3$ yielding Seifert fiber spaces. The basic idea is finding relationships among such surgeries. To describe relationships and get a global picture of Seifert surgeries, they introduce ``seiferters'' and the Seifert Surgery Network, a $1$-dimensional complex whose vertices correspond to Seifert surgeries. A seiferter for a Seifert surgery on a knot $K$ is a trivial knot in $S^3$ disjoint from $K$ that becomes a fiber in the resulting Seifert fiber space. Twisting $K$ along its seiferter or an annulus cobounded by a pair of its seiferters yields another knot admitting a Seifert surgery. Edges of the network correspond to such twistings. A path in the network from one Seifert surgery to another explains how the former Seifert surgery is obtained from the latter after a sequence of twistings along seiferters and/or annuli cobounded by pairs of seiferters. The authors find explicit paths from various known Seifert surgeries to those on torus knots, the most basic Seifert surgeries. The authors classify seiferters and obtain some fundamental results on the structure of the Seifert Surgery Network. From the networking viewpoint, they find an infinite family of Seifert surgeries on hyperbolic knots which cannot be embedded in a genus two Heegaard surface of $S^3$.