Cyclic Homology

Author : Jean-Louis Loday
Publisher : Springer Science & Business Media
ISBN 13 : 3662217392
Total Pages : 467 pages
Book Rating : 4.99/5 ( download)

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Download or read book Cyclic Homology written by Jean-Louis Loday and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a comprehensive study of cyclic homology theory together with its relationship with Hochschild homology, de Rham cohomology, S1 equivariant homology, the Chern character, Lie algebra homology, algebraic K-theory and non-commutative differential geometry. Though conceived as a basic reference on the subject, many parts of this book are accessible to graduate students.

Author : Ralph L. Cohen
Publisher : Springer Science & Business Media
ISBN 13 : 3764373881
Total Pages : 159 pages
Book Rating : 4.87/5 ( download)

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Download or read book String Topology and Cyclic Homology written by Ralph L. Cohen and published by Springer Science & Business Media. This book was released on 2006-03-21 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Joachim Cuntz
Publisher : Springer Science & Business Media
ISBN 13 : 9783540404699
Total Pages : 160 pages
Book Rating : 4.94/5 ( download)

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Download or read book Cyclic Homology in Non-Commutative Geometry written by Joachim Cuntz and published by Springer Science & Business Media. This book was released on 2003-11-17 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Joachim Cuntz
Publisher : Springer
ISBN 13 : 9783642073373
Total Pages : 0 pages
Book Rating : 4.79/5 ( download)

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Download or read book Cyclic Homology in Non-Commutative Geometry written by Joachim Cuntz and published by Springer. This book was released on 2011-01-23 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Jean-Louis Loday
Publisher : Springer Science & Business Media
ISBN 13 : 3662113899
Total Pages : 525 pages
Book Rating : 4.99/5 ( download)

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Download or read book Cyclic Homology written by Jean-Louis Loday and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Daniel G. Quillen
Publisher : Cambridge University Press
ISBN 13 : 1108479618
Total Pages : 331 pages
Book Rating : 4.15/5 ( download)

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Download or read book Topics in Cyclic Theory written by Daniel G. Quillen and published by Cambridge University Press. This book was released on 2020-07-09 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This accessible introduction for Ph.D. students and non-specialists provides Quillen's unique development of cyclic theory.

Author : Bjørn Ian Dundas
Publisher : Springer Science & Business Media
ISBN 13 : 1447143930
Total Pages : 447 pages
Book Rating : 4.32/5 ( download)

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Download or read book The Local Structure of Algebraic K-Theory written by Bjørn Ian Dundas and published by Springer Science & Business Media. This book was released on 2012-09-06 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic K-theory encodes important invariants for several mathematical disciplines, spanning from geometric topology and functional analysis to number theory and algebraic geometry. As is commonly encountered, this powerful mathematical object is very hard to calculate. Apart from Quillen's calculations of finite fields and Suslin's calculation of algebraically closed fields, few complete calculations were available before the discovery of homological invariants offered by motivic cohomology and topological cyclic homology. This book covers the connection between algebraic K-theory and Bökstedt, Hsiang and Madsen's topological cyclic homology and proves that the difference between the theories are ‘locally constant’. The usefulness of this theorem stems from being more accessible for calculations than K-theory, and hence a single calculation of K-theory can be used with homological calculations to obtain a host of ‘nearby’ calculations in K-theory. For instance, Quillen's calculation of the K-theory of finite fields gives rise to Hesselholt and Madsen's calculations for local fields, and Voevodsky's calculations for the integers give insight into the diffeomorphisms of manifolds. In addition to the proof of the full integral version of the local correspondence between K-theory and topological cyclic homology, the book provides an introduction to the necessary background in algebraic K-theory and highly structured homotopy theory; collecting all necessary tools into one common framework. It relies on simplicial techniques, and contains an appendix summarizing the methods widely used in the field. The book is intended for graduate students and scientists interested in algebraic K-theory, and presupposes a basic knowledge of algebraic topology.

Author : Sarah J. Witherspoon
Publisher : American Mathematical Society
ISBN 13 : 1470462869
Total Pages : 265 pages
Book Rating : 4.64/5 ( download)

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Download or read book Hochschild Cohomology for Algebras written by Sarah J. Witherspoon and published by American Mathematical Society. This book was released on 2020-06-30 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a thorough and self-contained introduction to the theory of Hochschild cohomology for algebras and includes many examples and exercises. The book then explores Hochschild cohomology as a Gerstenhaber algebra in detail, the notions of smoothness and duality, algebraic deformation theory, infinity structures, support varieties, and connections to Hopf algebra cohomology. Useful homological algebra background is provided in an appendix. The book is designed both as an introduction for advanced graduate students and as a resource for mathematicians who use Hochschild cohomology in their work.

Author : Haynes Miller
Publisher : CRC Press
ISBN 13 : 1351251600
Total Pages : 1043 pages
Book Rating : 4.00/5 ( download)

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Download or read book Handbook of Homotopy Theory written by Haynes Miller and published by CRC Press. This book was released on 2020-01-23 with total page 1043 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Homotopy Theory provides a panoramic view of an active area in mathematics that is currently seeing dramatic solutions to long-standing open problems, and is proving itself of increasing importance across many other mathematical disciplines. The origins of the subject date back to work of Henri Poincaré and Heinz Hopf in the early 20th century, but it has seen enormous progress in the 21st century. A highlight of this volume is an introduction to and diverse applications of the newly established foundational theory of ¥ -categories. The coverage is vast, ranging from axiomatic to applied, from foundational to computational, and includes surveys of applications both geometric and algebraic. The contributors are among the most active and creative researchers in the field. The 22 chapters by 31 contributors are designed to address novices, as well as established mathematicians, interested in learning the state of the art in this field, whose methods are of increasing importance in many other areas.

Author : Dale Husemöller
Publisher :
ISBN 13 :
Total Pages : 134 pages
Book Rating : 4.72/5 ( download)

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Download or read book Lectures on Cyclic Homology written by Dale Husemöller and published by . This book was released on 1991 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: