Metrics Connections And Gluing Theorems

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Metrics, Connections and Gluing Theorems

Author : Clifford Taubes
Publisher : American Mathematical Soc.
ISBN 13 : 0821803239
Total Pages : 98 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Metrics, Connections and Gluing Theorems by : Clifford Taubes

Download or read book Metrics, Connections and Gluing Theorems written by Clifford Taubes and published by American Mathematical Soc.. This book was released on 1996 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 is 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.

Riemannian Holonomy Groups and Calibrated Geometry

Author : Dominic D. Joyce
Publisher : Oxford University Press
ISBN 13 : 019921560X
Total Pages : 314 pages
Book Rating : 4.1/5 (992 download)

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Book Synopsis Riemannian Holonomy Groups and Calibrated Geometry by : Dominic D. Joyce

Download or read book Riemannian Holonomy Groups and Calibrated Geometry written by Dominic D. Joyce and published by Oxford University Press. This book was released on 2007 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Compact Manifolds with Special Holonomy

Author : Dominic D. Joyce
Publisher : OUP Oxford
ISBN 13 : 9780198506010
Total Pages : 460 pages
Book Rating : 4.5/5 (6 download)

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Book Synopsis Compact Manifolds with Special Holonomy by : Dominic D. Joyce

Download or read book Compact Manifolds with Special Holonomy written by Dominic D. Joyce and published by OUP Oxford. This book was released on 2000 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Grid Homology for Knots and Links

Author : Peter S. Ozsvath
Publisher : American Mathematical Soc.
ISBN 13 : 1470434423
Total Pages : 410 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Grid Homology for Knots and Links by : Peter S. Ozsvath

Download or read book Grid Homology for Knots and Links written by Peter S. Ozsvath and published by American Mathematical Soc.. This book was released on 2017-01-19 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Algebraic Geometry Santa Cruz 1995

Author : János Kollár
Publisher : American Mathematical Soc.
ISBN 13 : 0821808958
Total Pages : 473 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Algebraic Geometry Santa Cruz 1995 by : János Kollár

Download or read book Algebraic Geometry Santa Cruz 1995 written by János Kollár and published by American Mathematical Soc.. This book was released on 1997 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Gauge Theory and the Topology of Four-Manifolds

Author : Robert Friedman, John W. Morgan
Publisher : American Mathematical Soc.
ISBN 13 : 9780821886861
Total Pages : 236 pages
Book Rating : 4.8/5 (868 download)

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

Download or read book Gauge Theory and the Topology of Four-Manifolds written by Robert Friedman, John W. Morgan and published by American Mathematical Soc.. This book was released on with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is part of the IAS/Park City Mathematics series and focuses on gauge theory and the topology of four-manifolds.

Geometric Analysis

Author : Jingyi Chen
Publisher : Springer Nature
ISBN 13 : 3030349535
Total Pages : 616 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Geometric Analysis by : Jingyi Chen

Download or read book Geometric Analysis written by Jingyi Chen and published by Springer Nature. This book was released on 2020-04-10 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Families of Riemann Surfaces and Weil-Petersson Geometry

Author : Scott A. Wolpert
Publisher : American Mathematical Soc.
ISBN 13 : 0821849867
Total Pages : 130 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Families of Riemann Surfaces and Weil-Petersson Geometry by : Scott A. Wolpert

Download or read book Families of Riemann Surfaces and Weil-Petersson Geometry written by Scott A. Wolpert and published by American Mathematical Soc.. This book was released on 2010 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Topology, $C^*$-Algebras, and String Duality

Author : Jonathan R_osenberg
Publisher : American Mathematical Soc.
ISBN 13 : 0821849220
Total Pages : 122 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Topology, $C^*$-Algebras, and String Duality by : Jonathan R_osenberg

Download or read book Topology, $C^*$-Algebras, and String Duality written by Jonathan R_osenberg and published by American Mathematical Soc.. This book was released on 2009-10-27 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Topics in the Homological Theory of Modules Over Commutative Rings

Author : Melvin Hochster
Publisher : American Mathematical Soc.
ISBN 13 : 0821816748
Total Pages : 86 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Topics in the Homological Theory of Modules Over Commutative Rings by : Melvin Hochster

Download or read book Topics in the Homological Theory of Modules Over Commutative Rings written by Melvin Hochster and published by American Mathematical Soc.. This book was released on 1975 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

From Riches to Raags: 3-Manifolds, Right-Angled Artin Groups, and Cubical Geometry

Author : Daniel T. Wise
Publisher : American Mathematical Soc.
ISBN 13 : 0821888005
Total Pages : 161 pages
Book Rating : 4.8/5 (218 download)

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

Download or read book From Riches to Raags: 3-Manifolds, Right-Angled Artin Groups, and Cubical Geometry written by Daniel T. Wise and published by American Mathematical Soc.. This book was released on 2012 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).

From the Basic Homotopy Lemma to the Classification of C*-algebras

Author : Huaxin Lin
Publisher : American Mathematical Soc.
ISBN 13 : 1470434903
Total Pages : 240 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis From the Basic Homotopy Lemma to the Classification of C*-algebras by : Huaxin Lin

Download or read book From the Basic Homotopy Lemma to the Classification of C*-algebras written by Huaxin Lin and published by American Mathematical Soc.. This book was released on 2017-08-11 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Rudiments of Ramsey Theory

Author : Ron Graham
Publisher : American Mathematical Soc.
ISBN 13 : 0821841564
Total Pages : 82 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Rudiments of Ramsey Theory by : Ron Graham

Download or read book Rudiments of Ramsey Theory written by Ron Graham and published by American Mathematical Soc.. This book was released on 2015-10-01 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Floer Homology, Gauge Theory, and Low-Dimensional Topology

Author : Clay Mathematics Institute. Summer School
Publisher : American Mathematical Soc.
ISBN 13 : 9780821838457
Total Pages : 318 pages
Book Rating : 4.8/5 (384 download)

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

Download or read book Floer Homology, Gauge Theory, and Low-Dimensional Topology written by Clay Mathematics Institute. Summer School and published by American Mathematical Soc.. This book was released on 2006 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).

Tropical Geometry and Mirror Symmetry

Author : Mark Gross
Publisher : American Mathematical Soc.
ISBN 13 : 0821852329
Total Pages : 338 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Tropical Geometry and Mirror Symmetry by : Mark Gross

Download or read book Tropical Geometry and Mirror Symmetry written by Mark Gross and published by American Mathematical Soc.. This book was released on 2011-01-20 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Deformation Theory of Algebras and Their Diagrams

Author : Martin Markl
Publisher : American Mathematical Soc.
ISBN 13 : 0821889796
Total Pages : 129 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Deformation Theory of Algebras and Their Diagrams by : Martin Markl

Download or read book Deformation Theory of Algebras and Their Diagrams written by Martin Markl and published by American Mathematical Soc.. This book was released on 2012 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together both the classical and current aspects of deformation theory. The presentation is mostly self-contained, assuming only basic knowledge of commutative algebra, homological algebra and category theory. In the interest of readability, some technically complicated proofs have been omitted when a suitable reference was available. The relation between the uniform continuity of algebraic maps and topologized tensor products is explained in detail, however, as this subject does not seem to be commonly known and the literature is scarce. The exposition begins by recalling Gerstenhaber's classical theory for associative algebras. The focus then shifts to a homotopy-invariant setup of Maurer-Cartan moduli spaces. As an application, Kontsevich's approach to deformation quantization of Poisson manifolds is reviewed. Then, after a brief introduction to operads, a strongly homotopy Lie algebra governing deformations of (diagrams of) algebras of a given type is described, followed by examples and generalizations.

Single Orbit Dynamics

Author : Benjamin Weiss
Publisher : American Mathematical Soc.
ISBN 13 : 9780821889398
Total Pages : 132 pages
Book Rating : 4.8/5 (893 download)

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Book Synopsis Single Orbit Dynamics by : Benjamin Weiss

Download or read book Single Orbit Dynamics written by Benjamin Weiss and published by American Mathematical Soc.. This book was released on with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the expanded notes from ten lectures given by the author at the NSF/CBMS conference held at California State University (Bakersfield). The author describes what he calls single orbit dynamics, which is an approach to the analysis of dynamical systems via the study of single orbits, rather than the study of a system as a whole. He presents single orbit interpretations of several areas of topological dynamics and ergodic theory and some new applications of dynamics to graph theory. In the concluding lectures, single orbit approaches to generalizations of the Shannon-Breiman-McMillan theorem and related problems of compression and universal coding are presented. Complete proofs and illuminating discussions are included and references for further study are given. Some of the material appears here for the first time in print.