Metrics Connections And Gluing Theorems

Author : Clifford Taubes
Publisher : American Mathematical Soc.
Page : 90 pages
File Size : 54,7 Mb
Release : 1996
Category : Science
ISBN : 9780821803233

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Metrics, Connections and Gluing Theorems by Clifford Taubes Pdf

In this book, the author's goal is to provide an introduction to some of the analytic underpinnings for the geometry of anti-self duality in 4-dimensions. Anti-self duality is rather special to 4-dimensions and the imposition of this condition on curvatures of connections on vector bundles and on curvatures of Riemannian metrics has resulted in some spectacular mathematics. The book reviews some basic geometry, but it is assumed that the reader has a general background in differential geometry (as would be obtained by reading a standard text on the subject). Some of the fundamental references include Atiyah, Hitchin and Singer, Freed and Uhlenbeck, Donaldson and Kronheimer, and Kronheimer and Mrowka. The last chapter contains open problems and conjectures.

Author : Dominic D. Joyce
Publisher : Oxford University Press
Page : 314 pages
File Size : 43,9 Mb
Release : 2007
Category : Mathematics
ISBN : 9780199215607

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Riemannian Holonomy Groups and Calibrated Geometry by Dominic D. Joyce Pdf

Covering an exciting and active area of research at the crossroads of several different fields in mathematics and physics, and drawing on the author's previous work, this text has been written to explain the advanced mathematics involved simply and clearly to graduate students in both disciplines.

Author : Dominic D. Joyce
Publisher : OUP Oxford
Page : 460 pages
File Size : 45,5 Mb
Release : 2000
Category : Mathematics
ISBN : 0198506015

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Compact Manifolds with Special Holonomy by Dominic D. Joyce Pdf

This is a combination of a graduate textbook on Reimannian holonomy groups, and a research monograph on compact manifolds with the exceptional holonomy groups G2 and Spin (7). It contains much new research and many new examples.

Author : János Kollár,David R. Morrison
Publisher : American Mathematical Soc.
Page : 473 pages
File Size : 54,6 Mb
Release : 1997
Category : Geometry, Algebraic
ISBN : 9780821808955

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Algebraic Geometry Santa Cruz 1995 by János Kollár,David R. Morrison Pdf

Author : Peter S. Ozsvath,András I. Stipsicz,Zoltan Szabo
Publisher : American Mathematical Soc.
Page : 410 pages
File Size : 42,9 Mb
Release : 2017-01-19
Category : Education
ISBN : 9781470434427

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Grid Homology for Knots and Links by Peter S. Ozsvath,András I. Stipsicz,Zoltan Szabo Pdf

Knot theory is a classical area of low-dimensional topology, directly connected with the theory of three-manifolds and smooth four-manifold topology. In recent years, the subject has undergone transformative changes thanks to its connections with a number of other mathematical disciplines, including gauge theory; representation theory and categorification; contact geometry; and the theory of pseudo-holomorphic curves. Starting from the combinatorial point of view on knots using their grid diagrams, this book serves as an introduction to knot theory, specifically as it relates to some of the above developments. After a brief overview of the background material in the subject, the book gives a self-contained treatment of knot Floer homology from the point of view of grid diagrams. Applications include computations of the unknotting number and slice genus of torus knots (asked first in the 1960s and settled in the 1990s), and tools to study variants of knot theory in the presence of a contact structure. Additional topics are presented to prepare readers for further study in holomorphic methods in low-dimensional topology, especially Heegaard Floer homology. The book could serve as a textbook for an advanced undergraduate or part of a graduate course in knot theory. Standard background material is sketched in the text and the appendices.

Author : Robert Friedman, John W. Morgan
Publisher : American Mathematical Soc.
Page : 236 pages
File Size : 47,9 Mb
Release : 2024-06-02
Category : Four-manifolds (Topology).
ISBN : 082188686X

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Gauge Theory and the Topology of Four-Manifolds by Robert Friedman, John W. Morgan Pdf

This text is part of the IAS/Park City Mathematics series and focuses on gauge theory and the topology of four-manifolds.

Author : Jingyi Chen,Peng Lu,Zhiqin Lu,Zhou Zhang
Publisher : Springer Nature
Page : 616 pages
File Size : 44,6 Mb
Release : 2020-04-10
Category : Mathematics
ISBN : 9783030349530

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Geometric Analysis by Jingyi Chen,Peng Lu,Zhiqin Lu,Zhou Zhang Pdf

This edited volume has a two-fold purpose. First, comprehensive survey articles provide a way for beginners to ease into the corresponding sub-fields. These are then supplemented by original works that give the more advanced readers a glimpse of the current research in geometric analysis and related PDEs. The book is of significant interest for researchers, including advanced Ph.D. students, working in geometric analysis. Readers who have a secondary interest in geometric analysis will benefit from the survey articles. The results included in this book will stimulate further advances in the subjects: geometric analysis, including complex differential geometry, symplectic geometry, PDEs with a geometric origin, and geometry related to topology. Contributions by Claudio Arezzo, Alberto Della Vedova, Werner Ballmann, Henrik Matthiesen, Panagiotis Polymerakis, Sun-Yung A. Chang, Zheng-Chao Han, Paul Yang, Tobias Holck Colding, William P. Minicozzi II, Panagiotis Dimakis, Richard Melrose, Akito Futaki, Hajime Ono, Jiyuan Han, Jeff A. Viaclovsky, Bruce Kleiner, John Lott, Sławomir Kołodziej, Ngoc Cuong Nguyen, Chi Li, Yuchen Liu, Chenyang Xu, YanYan Li, Luc Nguyen, Bo Wang, Shiguang Ma, Jie Qing, Xiaonan Ma, Sean Timothy Paul, Kyriakos Sergiou, Tristan Rivière, Yanir A. Rubinstein, Natasa Sesum, Jian Song, Jeffrey Streets, Neil S. Trudinger, Yu Yuan, Weiping Zhang, Xiaohua Zhu and Aleksey Zinger.

Author : Scott A. Wolpert
Publisher : American Mathematical Soc.
Page : 130 pages
File Size : 48,7 Mb
Release : 2010
Category : Ergodic theory
ISBN : 9780821849866

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Families of Riemann Surfaces and Weil-Petersson Geometry by Scott A. Wolpert Pdf

Provides a generally self-contained course for graduate students and postgraduates on deformations of hyperbolic surfaces and the geometry of the Weil-Petersson metric. It also offers an update for researchers; material not otherwise found in a single reference is included; and aunified approach is provided for an array of results.

Author : Jonathan R_osenberg
Publisher : American Mathematical Soc.
Page : 110 pages
File Size : 44,9 Mb
Release : 2009-10-27
Category : Mathematics
ISBN : 9780821849224

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Topology, C*-algebras, and String Duality by Jonathan R_osenberg Pdf

String theory is the leading candidate for a physical theory that combines all the fundamental forces of nature, as well as the principles of relativity and quantum mechanics, into a mathematically elegant whole. The mathematical tools used by string theorists are highly sophisticated, and cover many areas of mathematics. As with the birth of quantum theory in the early 20th century, the mathematics has benefited at least as much as the physics from the collaboration. In this book, based on CBMS lectures given at Texas Christian University, Rosenberg describes some of the most recent interplay between string dualities and topology and operator algebras. The book is an interdisciplinary approach to duality symmetries in string theory. It can be read by either mathematicians or theoretical physicists, and involves a more-or-less equal mixture of algebraic topology, operator algebras, and physics. There is also a bit of algebraic geometry, especially in the last chapter. The reader is assumed to be somewhat familiar with at least one of these four subjects, but not necessarily with all or even most of them. The main objective of the book is to show how several seemingly disparate subjects are closely linked with one another, and to give readers an overview of some areas of current research, even if this means that not everything is covered systematically.

Author : Melvin Hochster
Publisher : American Mathematical Soc.
Page : 86 pages
File Size : 43,5 Mb
Release : 1975
Category : Mathematics
ISBN : 9780821816745

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Topics in the Homological Theory of Modules Over Commutative Rings by Melvin Hochster Pdf

Contains expository lectures from the CBMS Regional Conference in Mathematics held at the University of Nebraska, June 1974. This book deals mainly with developments and still open questions in the homological theory of modules over commutative (usually, Noetherian) rings.

Author : Daniel T. Wise
Publisher : American Mathematical Soc.
Page : 161 pages
File Size : 46,6 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821888001

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From Riches to Raags: 3-Manifolds, Right-Angled Artin Groups, and Cubical Geometry by Daniel T. Wise Pdf

Wise describes a stream of geometric group theory connecting many of the classically considered groups arising in combinatorial group theory with right-angled Artin groups. He writes for new or seasoned researchers who have completed at least an introductory course of geometric groups theory or even just hyperbolic groups, but says some comfort with graphs of groups would be helpful. His topics include non-positively curved cube complexes, virtual specialness of malnormal amalgams, finiteness properties of the dual cube complex, walls in cubical small-cancellation theory, and hyperbolicity and quasiconvexity detection. Color drawings illustrate. Annotation ©2013 Book News, Inc., Portland, OR (booknews.com).

Author : Huaxin Lin
Publisher : American Mathematical Soc.
Page : 240 pages
File Size : 49,8 Mb
Release : 2017-08-11
Category : C*-algebras
ISBN : 9781470434908

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From the Basic Homotopy Lemma to the Classification of C*-algebras by Huaxin Lin Pdf

This book examines some recent developments in the theory of -algebras, which are algebras of operators on Hilbert spaces. An elementary introduction to the technical part of the theory is given via a basic homotopy lemma concerning a pair of almost commuting unitaries. The book presents an outline of the background as well as some recent results of the classification of simple amenable -algebras, otherwise known as the Elliott program. This includes some stable uniqueness theorems and a revisiting of Bott maps via stable homotopy. Furthermore, -theory related rotation maps are introduced. The book is based on lecture notes from the CBMS lecture sequence at the University of Wyoming in the summer of 2015.

Author : Ron Graham, Steve Butler
Publisher : American Mathematical Soc.
Page : 82 pages
File Size : 48,6 Mb
Release : 2015-10-01
Category : Combinatorial analysis
ISBN : 9780821841563

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Rudiments of Ramsey Theory by Ron Graham, Steve Butler Pdf

In every sufficiently large structure which has been partitioned there will always be some well-behaved structure in one of the parts. This takes many forms. For example, colorings of the integers by finitely many colors must have long monochromatic arithmetic progressions (van der Waerden's theorem); and colorings of the edges of large graphs must have monochromatic subgraphs of a specified type (Ramsey's theorem). This book explores many of the basic results and variations of this theory. Since the first edition of this book there have been many advances in this field. In the second edition the authors update the exposition to reflect the current state of the art. They also include many pointers to modern results. A co-publication of the AMS and CBMS.

Author : Clay Mathematics Institute. Summer School
Publisher : American Mathematical Soc.
Page : 318 pages
File Size : 42,7 Mb
Release : 2006
Category : Mathematics
ISBN : 0821838458

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Floer Homology, Gauge Theory, and Low-Dimensional Topology by Clay Mathematics Institute. Summer School Pdf

Mathematical gauge theory studies connections on principal bundles, or, more precisely, the solution spaces of certain partial differential equations for such connections. Historically, these equations have come from mathematical physics, and play an important role in the description of the electro-weak and strong nuclear forces. The use of gauge theory as a tool for studying topological properties of four-manifolds was pioneered by the fundamental work of Simon Donaldson in theearly 1980s, and was revolutionized by the introduction of the Seiberg-Witten equations in the mid-1990s. Since the birth of the subject, it has retained its close connection with symplectic topology. The analogy between these two fields of study was further underscored by Andreas Floer's constructionof an infinite-dimensional variant of Morse theory that applies in two a priori different contexts: either to define symplectic invariants for pairs of Lagrangian submanifolds of a symplectic manifold, or to define topological This volume is based on lecture courses and advanced seminars given at the 2004 Clay Mathematics Institute Summer School at the Alfred Renyi Institute of Mathematics in Budapest, Hungary. Several of the authors have added a considerable amount of additional material tothat presented at the school, and the resulting volume provides a state-of-the-art introduction to current research, covering material from Heegaard Floer homology, contact geometry, smooth four-manifold topology, and symplectic four-manifolds. Information for our distributors: Titles in this seriesare copublished with the Clay Mathematics Institute (Cambridge, MA).

Author : Mark Gross
Publisher : American Mathematical Soc.
Page : 338 pages
File Size : 53,8 Mb
Release : 2011-01-20
Category : Mathematics
ISBN : 9780821852323

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Tropical Geometry and Mirror Symmetry by Mark Gross Pdf

Tropical geometry provides an explanation for the remarkable power of mirror symmetry to connect complex and symplectic geometry. The main theme of this book is the interplay between tropical geometry and mirror symmetry, culminating in a description of the recent work of Gross and Siebert using log geometry to understand how the tropical world relates the A- and B-models in mirror symmetry. The text starts with a detailed introduction to the notions of tropical curves and manifolds, and then gives a thorough description of both sides of mirror symmetry for projective space, bringing together material which so far can only be found scattered throughout the literature. Next follows an introduction to the log geometry of Fontaine-Illusie and Kato, as needed for Nishinou and Siebert's proof of Mikhalkin's tropical curve counting formulas. This latter proof is given in the fourth chapter. The fifth chapter considers the mirror, B-model side, giving recent results of the author showing how tropical geometry can be used to evaluate the oscillatory integrals appearing. The final chapter surveys reconstruction results of the author and Siebert for ``integral tropical manifolds.'' A complete version of the argument is given in two dimensions.