Cyclic Homology In Non Commutative Geometry
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Cyclic Homology In Non Commutative Geometry
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Author : Joachim Cuntz
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-11-17
Cyclic Homology In Non Commutative Geometry written by Joachim Cuntz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-11-17 with Mathematics categories.
Contributions by three authors treat aspects of noncommutative geometry that are related to cyclic homology. The authors give rather complete accounts of cyclic theory from different points of view. The connections between (bivariant) K-theory and cyclic theory via generalized Chern-characters are discussed in detail. Cyclic theory is the natural setting for a variety of general abstract index theorems. A survey of such index theorems is given and the concepts and ideas involved in these theorems are explained.
Cyclic Homology In Non Commutative Geometry
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Author : Joachim Cuntz
language : en
Publisher: Springer
Release Date : 2014-01-15
Cyclic Homology In Non Commutative Geometry written by Joachim Cuntz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Contributions by three authors treat aspects of noncommutative geometry that are related to cyclic homology. The authors give rather complete accounts of cyclic theory from different points of view. The connections between (bivariant) K-theory and cyclic theory via generalized Chern-characters are discussed in detail. Cyclic theory is the natural setting for a variety of general abstract index theorems. A survey of such index theorems is given and the concepts and ideas involved in these theorems are explained.
Cyclic Cohomology And Noncommutative Geometry
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Author : Joachim J. R. Cuntz
language : en
Publisher: American Mathematical Soc.
Release Date : 1997-01-01
Cyclic Cohomology And Noncommutative Geometry written by Joachim J. R. Cuntz 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 1997-01-01 with Mathematics categories.
Noncommutative geometry is a new field that is among the great challenges of present-day mathematics. Its methods allow one to treat noncommutative algebras - such as algebras of pseudodifferential operators, group algebras, or algebras arising from quantum field theory - on the same footing as commutative algebras, that is, as spaces. Applications range over many fields of mathematics and mathematical physics. This volume contains the proceedings of the workshop on "Cyclic Cohomology and Noncommutative Geometry" held at The Fields Institute (Waterloo, ON) in June 1995. The workshop was part of the program for the special year on operator algebras and its applications.
K Theory And Noncommutative Geometry
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Author : Guillermo Cortiñas
language : en
Publisher: European Mathematical Society
Release Date : 2008
K Theory And Noncommutative Geometry written by Guillermo Cortiñas and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with K-theory categories.
Since its inception 50 years ago, K-theory has been a tool for understanding a wide-ranging family of mathematical structures and their invariants: topological spaces, rings, algebraic varieties and operator algebras are the dominant examples. The invariants range from characteristic classes in cohomology, determinants of matrices, Chow groups of varieties, as well as traces and indices of elliptic operators. Thus K-theory is notable for its connections with other branches of mathematics. Noncommutative geometry develops tools which allow one to think of noncommutative algebras in the same footing as commutative ones: as algebras of functions on (noncommutative) spaces. The algebras in question come from problems in various areas of mathematics and mathematical physics; typical examples include algebras of pseudodifferential operators, group algebras, and other algebras arising from quantum field theory. To study noncommutative geometric problems one considers invariants of the relevant noncommutative algebras. These invariants include algebraic and topological K-theory, and also cyclic homology, discovered independently by Alain Connes and Boris Tsygan, which can be regarded both as a noncommutative version of de Rham cohomology and as an additive version of K-theory. There are primary and secondary Chern characters which pass from K-theory to cyclic homology. These characters are relevant both to noncommutative and commutative problems and have applications ranging from index theorems to the detection of singularities of commutative algebraic varieties. The contributions to this volume represent this range of connections between K-theory, noncommmutative geometry, and other branches of mathematics.
Noncommutative Geometry And Number Theory
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Author : Caterina Consani
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-18
Noncommutative Geometry And Number Theory written by Caterina Consani and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-18 with Mathematics categories.
In recent years, number theory and arithmetic geometry have been enriched by new techniques from noncommutative geometry, operator algebras, dynamical systems, and K-Theory. This volume collects and presents up-to-date research topics in arithmetic and noncommutative geometry and ideas from physics that point to possible new connections between the fields of number theory, algebraic geometry and noncommutative geometry. The articles collected in this volume present new noncommutative geometry perspectives on classical topics of number theory and arithmetic such as modular forms, class field theory, the theory of reductive p-adic groups, Shimura varieties, the local L-factors of arithmetic varieties. They also show how arithmetic appears naturally in noncommutative geometry and in physics, in the residues of Feynman graphs, in the properties of noncommutative tori, and in the quantum Hall effect.
Perspectives On Noncommutative Geometry
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Author : Masoud Khalkhali
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
Perspectives On Noncommutative Geometry written by Masoud Khalkhali 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 2011 with Algebra, Homological categories.
This volume represents the proceedings of the Noncommutative Geometry Workshop that was held as part of the thematic program on operator algebras at the Fields Institute in May 2008. Pioneered by Alain Connes starting in the late 1970s, noncommutative geometry was originally inspired by global analysis, topology, operator algebras, and quantum physics. Its main applications were to settle some long-standing conjectures, such as the Novikov conjecture and the Baum-Connes conjecture. Next came the impact of spectral geometry and the way the spectrum of a geometric operator, like the Laplacian, holds information about the geometry and topology of a manifold, as in the celebrated Weyl law. This has now been vastly generalized through Connes' notion of spectral triples. Finally, recent years have witnessed the impact of number theory, algebraic geometry and the theory of motives, and quantum field theory on noncommutative geometry. Almost all of these aspects are touched upon with new results in the papers of this volume. This book is intended for graduate students and researchers in both mathematics and theoretical physics who are interested in noncommutative geometry and its applications.
Local And Analytic Cyclic Homology
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Author : Ralf Meyer
language : en
Publisher: European Mathematical Society
Release Date : 2007
Local And Analytic Cyclic Homology written by Ralf Meyer and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
Periodic cyclic homology is a homology theory for non-commutative algebras that plays a similar role in non-commutative geometry as de Rham cohomology for smooth manifolds. While it produces good results for algebras of smooth or polynomial functions, it fails for bigger algebras such as most Banach algebras or C*-algebras. Analytic and local cyclic homology are variants of periodic cyclic homology that work better for such algebras. In this book, the author develops and compares these theories, emphasizing their homological properties. This includes the excision theorem, invariance under passage to certain dense subalgebras, a Universal Coefficient Theorem that relates them to $K$-theory, and the Chern-Connes character for $K$-theory and $K$-homology. The cyclic homology theories studied in this text require a good deal of functional analysis in bornological vector spaces, which is supplied in the first chapters. The focal points here are the relationship with inductive systems and the functional calculus in non-commutative bornological algebras. Some chapters are more elementary and independent of the rest of the book and will be of interest to researchers and students working on functional analysis and its applications.
Cyclic Homology
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Author : Jean-Louis Loday
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Cyclic Homology written by Jean-Louis Loday and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
From the reviews: "This is a very interesting book containing material for a comprehensive study of the cyclid homological theory of algebras, cyclic sets and S1-spaces. Lie algebras and algebraic K-theory and an introduction to Connes'work and recent results on the Novikov conjecture. The book requires a knowledge of homological algebra and Lie algebra theory as well as basic technics coming from algebraic topology. The bibliographic comments at the end of each chapter offer good suggestions for further reading and research. The book can be strongly recommended to anybody interested in noncommutative geometry, contemporary algebraic topology and related topics." European Mathematical Society Newsletter In this second edition the authors have added a chapter 13 on MacLane (co)homology.
Basic Noncommutative Geometry
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Author : Masoud Khalkhali
language : en
Publisher: European Mathematical Society
Release Date : 2009
Basic Noncommutative Geometry written by Masoud Khalkhali and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
"Basic Noncommutative Geometry provides an introduction to noncommutative geometry and some of its applications. The book can be used either as a textbook for a graduate course on the subject or for self-study. It will be useful for graduate students and researchers in mathematics and theoretical physics and all those who are interested in gaining an understanding of the subject. One feature of this book is the wealth of examples and exercises that help the reader to navigate through the subject. While background material is provided in the text and in several appendices, some familiarity with basic notions of functional analysis, algebraic topology, differential geometry and homological algebra at a first year graduate level is helpful. Developed by Alain Connes since the late 1970s, noncommutative geometry has found many applications to long-standing conjectures in topology and geometry and has recently made headways in theoretical physics and number theory. The book starts with a detailed description of some of the most pertinent algebra-geometry correspondences by casting geometric notions in algebraic terms, then proceeds in the second chapter to the idea of a noncommutative space and how it is constructed. The last two chapters deal with homological tools: cyclic cohomology and Connes-Chern characters in K-theory and K-homology, culminating in one commutative diagram expressing the equality of topological and analytic index in a noncommutative setting. Applications to integrality of noncommutative topological invariants are given as well."--Publisher's description.
Cyclic Homology In Non Commutative Geometry
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Author : Joachim Cuntz
language : en
Publisher: Springer
Release Date : 2011-01-23
Cyclic Homology In Non Commutative Geometry written by Joachim Cuntz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-23 with Mathematics categories.
Contributions by three authors treat aspects of noncommutative geometry that are related to cyclic homology. The authors give rather complete accounts of cyclic theory from different points of view. The connections between (bivariant) K-theory and cyclic theory via generalized Chern-characters are discussed in detail. Cyclic theory is the natural setting for a variety of general abstract index theorems. A survey of such index theorems is given and the concepts and ideas involved in these theorems are explained.