From The Basic Homotopy Lemma To The Classification Of C Algebras
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From The Basic Homotopy Lemma To The Classification Of C Algebras
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Author : Huaxin Lin
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-08-11
From The Basic Homotopy Lemma To The Classification Of C Algebras written by Huaxin Lin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-11 with C*-algebras categories.
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.
Approximate Homotopy Of Homomorphisms From C X Into A Simple C Algebra
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Author : Huaxin Lin
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Approximate Homotopy Of Homomorphisms From C X Into A Simple C Algebra written by Huaxin Lin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
"Volume 205, number 963 (second of 5 numbers)."
Algebraic Homotopy
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Author : Hans J. Baues
language : en
Publisher: Cambridge University Press
Release Date : 1989-02-16
Algebraic Homotopy written by Hans J. Baues and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-02-16 with Mathematics categories.
This book gives a general outlook on homotopy theory; fundamental concepts, such as homotopy groups and spectral sequences, are developed from a few axioms and are thus available in a broad variety of contexts. Many examples and applications in topology and algebra are discussed, including an introduction to rational homotopy theory in terms of both differential Lie algebras and De Rham algebras. The author describes powerful tools for homotopy classification problems, particularly for the classification of homotopy types and for the computation of the group homotopy equivalences. Applications and examples of such computations are given, including when the fundamental group is non-trivial. Moreover, the deep connection between the homotopy classification problems and the cohomology theory of small categories is demonstrated. The prerequisites of the book are few: elementary topology and algebra. Consequently, this account will be valuable for non-specialists and experts alike. It is an important supplement to the standard presentations of algebraic topology, homotopy theory, category theory and homological algebra.
Classification Of Mathcal O Infty Stable C Algebras
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Author : James Gabe
language : en
Publisher: American Mathematical Society
Release Date : 2024-02-01
Classification Of Mathcal O Infty Stable C Algebras written by James Gabe and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-01 with Mathematics categories.
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Effective Algebraic Topology
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Author : Rolf Schön
language : en
Publisher: American Mathematical Soc.
Release Date : 1991
Effective Algebraic Topology written by Rolf Schön and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
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The Classification And Structure Of C Algebra Bundles
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Author : Maurice J. Dupré
language : en
Publisher: American Mathematical Soc.
Release Date : 1979
The Classification And Structure Of C Algebra Bundles written by Maurice J. Dupré and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Mathematics categories.
The objects of study in this paper are certain fibre spaces which arise naturally in the representation theory of C*-algebras and locally compact groups. These are a type of Banach bundle, all of whose fibres are C*-algebras. The main aim of this paper is to give a pasting homotopy type classification theory for certain classes of C*-bundles having primarily finite-dimensional fibres and thus classifying the resulting second-order bundles.
Tensors Asymptotic Geometry And Developments 2016 2018
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Author : J.M. Landsberg
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-07-05
Tensors Asymptotic Geometry And Developments 2016 2018 written by J.M. Landsberg and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-05 with Calculus of tensors categories.
Tensors are used throughout the sciences, especially in solid state physics and quantum information theory. This book brings a geometric perspective to the use of tensors in these areas. It begins with an introduction to the geometry of tensors and provides geometric expositions of the basics of quantum information theory, Strassen's laser method for matrix multiplication, and moment maps in algebraic geometry. It also details several exciting recent developments regarding tensors in general. In particular, it discusses and explains the following material previously only available in the original research papers: (1) Shitov's 2017 refutation of longstanding conjectures of Strassen on rank additivity and Common on symmetric rank; (2) The 2017 Christandl-Vrana-Zuiddam quantum spectral points that bring together quantum information theory, the asymptotic geometry of tensors, matrix multiplication complexity, and moment polytopes in geometric invariant theory; (3) the use of representation theory in quantum information theory, including the solution of the quantum marginal problem; (4) the use of tensor network states in solid state physics, and (5) recent geometric paths towards upper bounds for the complexity of matrix multiplication. Numerous open problems appropriate for graduate students and post-docs are included throughout.
Mathematical Biology Modeling And Analysis
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Author : Avner Friedman
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-06-14
Mathematical Biology Modeling And Analysis written by Avner Friedman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-14 with Biology categories.
The fast growing field of mathematical biology addresses biological questions using mathematical models from areas such as dynamical systems, probability, statistics, and discrete mathematics. This book considers models that are described by systems of partial differential equations, and it focuses on modeling, rather than on numerical methods and simulations. The models studied are concerned with population dynamics, cancer, risk of plaque growth associated with high cholesterol, and wound healing. A rich variety of open problems demonstrates the exciting challenges and opportunities for research at the interface of mathematics and biology. This book primarily addresses students and researchers in mathematics who do not necessarily have any background in biology and who may have had little exposure to PDEs.
Introduction To The Theory Of Valuations
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Author : Semyon Alesker
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-06-27
Introduction To The Theory Of Valuations written by Semyon Alesker and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-27 with Graph labelings categories.
Theory of valuations on convex sets is a classical part of convex geometry which goes back at least to the positive solution of the third Hilbert problem by M. Dehn in 1900. Since then the theory has undergone a multifaceted development. The author discusses some of Hadwiger's results on valuations on convex compact sets that are continuous in the Hausdorff metric. The book also discusses the Klain-Schneider theorem as well as the proof of McMullen's conjecture, which led subsequently to many further applications and advances in the theory. The last section gives an overview of more recent developments in the theory of translation-invariant continuous valuations, some of which turn out to be useful in integral geometry. This book grew out of lectures that were given in August 2015 at Kent State University in the framework of the NSF CBMS conference “Introduction to the Theory of Valuations on Convex Sets”. Only a basic background in general convexity is assumed.
Lectures On Field Theory And Topology
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Author : Daniel S. Freed
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-08-23
Lectures On Field Theory And Topology written by Daniel S. Freed and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-23 with Algebraic topology categories.
These lectures recount an application of stable homotopy theory to a concrete problem in low energy physics: the classification of special phases of matter. While the joint work of the author and Michael Hopkins is a focal point, a general geometric frame of reference on quantum field theory is emphasized. Early lectures describe the geometric axiom systems introduced by Graeme Segal and Michael Atiyah in the late 1980s, as well as subsequent extensions. This material provides an entry point for mathematicians to delve into quantum field theory. Classification theorems in low dimensions are proved to illustrate the framework. The later lectures turn to more specialized topics in field theory, including the relationship between invertible field theories and stable homotopy theory, extended unitarity, anomalies, and relativistic free fermion systems. The accompanying mathematical explanations touch upon (higher) category theory, duals to the sphere spectrum, equivariant spectra, differential cohomology, and Dirac operators. The outcome of computations made using the Adams spectral sequence is presented and compared to results in the condensed matter literature obtained by very different means. The general perspectives and specific applications fuse into a compelling story at the interface of contemporary mathematics and theoretical physics.