Lectures On Cyclic Homology
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Lectures On Cyclic Homology
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Author : Dale Husemöller
language : en
Publisher:
Release Date : 1991
Lectures On Cyclic Homology written by Dale Husemöller and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Algebra, Homological categories.
Cyclic Homology In Non Commutative Geometry
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Author : Joachim Cuntz
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
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 2013-03-14 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.
Topics In Cyclic Theory
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Author : Daniel G. Quillen
language : en
Publisher: Cambridge University Press
Release Date : 2020-07-09
Topics In Cyclic Theory written by Daniel G. Quillen 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 2020-07-09 with Mathematics categories.
This accessible introduction for Ph.D. students and non-specialists provides Quillen's unique development of cyclic theory.
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.
Lectures On Factorization Homology Categories And Topological Field Theories
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Author : Hiro Lee Tanaka
language : en
Publisher: Springer Nature
Release Date : 2020-12-14
Lectures On Factorization Homology Categories And Topological Field Theories written by Hiro Lee Tanaka and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-14 with Science categories.
This book provides an informal and geodesic introduction to factorization homology, focusing on providing intuition through simple examples. Along the way, the reader is also introduced to modern ideas in homotopy theory and category theory, particularly as it relates to the use of infinity-categories. As with the original lectures, the text is meant to be a leisurely read suitable for advanced graduate students and interested researchers in topology and adjacent fields.
String Topology And Cyclic Homology
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Author : Ralph L. Cohen
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-21
String Topology And Cyclic Homology written by Ralph L. Cohen 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 2006-03-21 with Mathematics categories.
This book explores string topology, Hochschild and cyclic homology, assembling material from a wide scattering of scholarly sources in a single practical volume. The first part offers a thorough and elegant exposition of various approaches to string topology and the Chas-Sullivan loop product. The second gives a complete and clear construction of an algebraic model for computing topological cyclic 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.
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.
Lectures On Homology
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Author : Michel André
language : en
Publisher:
Release Date : 1970
Lectures On Homology written by Michel André and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Homology theory categories.
Topics In The Homology Theory Of Fibre Bundles
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Author : Armand Borel
language : en
Publisher: Springer
Release Date : 2006-11-14
Topics In The Homology Theory Of Fibre Bundles written by Armand Borel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.