Cyclic Homology in Non-Commutative Geometry PDF Download
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Author: Joachim Cuntz
Publisher: Springer Science & Business Media
ISBN: 9783540404699
Category : Mathematics
Languages : en
Pages : 160
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Book Description
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 Science & Business Media
ISBN: 9783540404699
Category : Mathematics
Languages : en
Pages : 160
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Book Description
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: 9783662064450
Category :
Languages : en
Pages : 156
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Book Description
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 J. R. Cuntz
Publisher: American Mathematical Soc.
ISBN: 9780821871249
Category : Mathematics
Languages : en
Pages : 202
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Book Description
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.
Author: Joachim Cuntz
Publisher: Springer Science & Business Media
ISBN: 3662064448
Category : Mathematics
Languages : en
Pages : 147
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Book Description
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: Alain Connes
Publisher: Springer
ISBN: 3540397027
Category : Mathematics
Languages : en
Pages : 364
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Book Description
Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.
Author:
Publisher:
ISBN:
Category : Geometry, Algebraic
Languages : en
Pages :
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Book Description
Author: Jean-Louis Loday
Publisher: Springer Science & Business Media
ISBN: 3662217392
Category : Mathematics
Languages : en
Pages : 467
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Book Description
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: Caterina Consani
Publisher: Springer Science & Business Media
ISBN: 3834803529
Category : Mathematics
Languages : en
Pages : 374
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Book Description
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.
Author: A. Connes
Publisher: American Mathematical Society
ISBN: 1470469774
Category : Mathematics
Languages : en
Pages : 592
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Book Description
This volume contains the proceedings of the virtual conference on Cyclic Cohomology at 40: Achievements and Future Prospects, held from September 27–October 1, 2021 and hosted by the Fields Institute for Research in Mathematical Sciences, Toronto, ON, Canada. Cyclic cohomology, since its discovery forty years ago in noncommutative differential geometry, has become a fundamental mathematical tool with applications in domains as diverse as analysis, algebraic K-theory, algebraic geometry, arithmetic geometry, solid state physics and quantum field theory. The reader will find survey articles providing a user-friendly introduction to applications of cyclic cohomology in such areas as higher categorical algebra, Hopf algebra symmetries, de Rham-Witt complex, quantum physics, etc., in which cyclic homology plays the role of a unifying theme. The researcher will find frontier research articles in which the cyclic theory provides a computational tool of great relevance. In particular, in analysis cyclic cohomology index formulas capture the higher invariants of manifolds, where the group symmetries are extended to Hopf algebra actions, and where Lie algebra cohomology is greatly extended to the cyclic cohomology of Hopf algebras which becomes the natural receptacle for characteristic classes. In algebraic topology the cyclotomic structure obtained using the cyclic subgroups of the circle action on topological Hochschild homology gives rise to remarkably significant arithmetic structures intimately related to crystalline cohomology through the de Rham-Witt complex, Fontaine's theory and the Fargues-Fontaine curve.
Author: Neculai S. Teleman
Publisher: Springer Nature
ISBN: 3030284336
Category : Mathematics
Languages : en
Pages : 398
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Book Description
This book aims to provide a friendly introduction to non-commutative geometry. It studies index theory from a classical differential geometry perspective up to the point where classical differential geometry methods become insufficient. It then presents non-commutative geometry as a natural continuation of classical differential geometry. It thereby aims to provide a natural link between classical differential geometry and non-commutative geometry. The book shows that the index formula is a topological statement, and ends with non-commutative topology.
