Higher Index Theory

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Higher Index Theory

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Author : Rufus Willett
language : en
Publisher: Cambridge University Press
Release Date : 2020-07-02

Higher Index Theory written by Rufus Willett 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 2020-07-02 with Mathematics categories.

A friendly introduction to higher index theory, a rapidly-developing subject at the intersection of geometry, topology and operator algebras. A well-balanced combination of introductory material (with exercises), cutting-edge developments and references to the wider literature make this book a valuable guide for graduate students and experts alike.

Index Theory Coarse Geometry And Topology Of Manifolds

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Author : John Roe
language : en
Publisher: American Mathematical Soc.
Release Date : 1996

Index Theory Coarse Geometry And Topology Of Manifolds written by John Roe 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 1996 with Mathematics categories.

Lecture notes from the conference held Aug. 1995 in Boulder, Colo.

Coarse Cohomology And Index Theory On Complete Riemannian Manifolds

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Author : John Roe
language : en
Publisher: American Mathematical Soc.
Release Date : 1993

Coarse Cohomology And Index Theory On Complete Riemannian Manifolds written by John Roe 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 1993 with Mathematics categories.

"July 1993, volume 104, number 497 (fourth of 6 numbers)."

Noncommutative Maslov Index And Eta Forms

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Author : Charlotte Wahl
language : en
Publisher: American Mathematical Soc.
Release Date : 2007

Noncommutative Maslov Index And Eta Forms written by Charlotte Wahl 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 2007 with Mathematics categories.

The author defines and proves a noncommutative generalization of a formula relating the Maslov index of a triple of Lagrangian subspaces of a symplectic vector space to eta-invariants associated to a pair of Lagrangian subspaces. The noncommutative Maslov index, defined for modules over a $C*$-algebra $\mathcal{A $, is an element in $K 0(\mathcal{A )$. The generalized formula calculates its Chern character in the de Rham homology of certain dense subalgebras of $\mathcal{A $. The proof is a noncommutative Atiyah-Patodi-Singer index theorem for a particular Dirac operator twisted by an $\mathcal{A $-vector bundle. The author develops an analytic framework for this type of index problem.

Perspectives In Scalar Curvature In 2 Volumes

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Author : Mikhail L Gromov
language : en
Publisher: World Scientific
Release Date : 2022-12-19

Perspectives In Scalar Curvature In 2 Volumes written by Mikhail L Gromov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-19 with Mathematics categories.

Volume I contains a long article by Misha Gromov based on his many years of involvement in this subject. It came from lectures delivered in Spring 2019 at IHES. There is some background given. Many topics in the field are presented, and many open problems are discussed. One intriguing point here is the crucial role played by two seemingly unrelated analytic means: index theory of Dirac operators and geometric measure theory.Very recently there have been some real breakthroughs in the field. Volume I has several survey articles written by people who were responsible for these results.For Volume II, many people in areas of mathematics and physics, whose work is somehow related to scalar curvature, were asked to write about this in any way they pleased. This gives rise to a wonderful collection of articles, some with very broad and historical views, others which discussed specific fascinating subjects.These two books give a rich and powerful view of one of geometry's very appealing sides.

Spectral Geometry Of Manifolds With Boundary And Decomposition Of Manifolds

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Author : Gerd Grubb
language : en
Publisher: American Mathematical Soc.
Release Date : 2005

Spectral Geometry Of Manifolds With Boundary And Decomposition Of Manifolds written by Gerd Grubb 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 2005 with Mathematics categories.

In recent years, increasingly complex methods have been brought into play in the treatment of geometric and topological problems for partial differential operators on manifolds. This collection of papers, resulting from a Workshop on Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds, provides a broad picture of these methods with new results. Subjects in the book cover a wide variety of topics, from recent advances in index theory and the more general boundary, to applications of those invariants in geometry, topology, and physics. Papers are grouped into four parts: Part I gives an overview of the subject from various points of view. Part II deals with spectral invariants, such as geometric and topological questions. Part IV deals specifically with problems on manifolds with singularities. The book is suitable for graduate students and researchers interested in spectral problems in geometry.

Export And Import Price Index Manual Theory And Practice

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Author : OECD
language : en
Publisher: OECD Publishing
Release Date : 2010-04-06

Export And Import Price Index Manual Theory And Practice written by OECD and has been published by OECD Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-04-06 with categories.

A joint production by six international organizations, this manual explores the conceptual and theoretical issues that national statistical offices should consider in the daily compilation of export and import price indices. Intended for use by both ...

Noncommutative Geometry And Physics 3 Proceedings Of The Noncommutative Geometry And Physics 2008 On K Theory And D Branes Proceedings Of The Rims Thematic Year 2010 On Perspectives In Deformation Quantization And Noncommutative Geometry

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Author : Giuseppe Dito
language : en
Publisher: World Scientific
Release Date : 2013-01-11

Noncommutative Geometry And Physics 3 Proceedings Of The Noncommutative Geometry And Physics 2008 On K Theory And D Branes Proceedings Of The Rims Thematic Year 2010 On Perspectives In Deformation Quantization And Noncommutative Geometry written by Giuseppe Dito and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-11 with Mathematics categories.

Noncommutative differential geometry is a novel approach to geometry, aimed in part at applications in physics. It was founded in the early eighties by the 1982 Fields Medalist Alain Connes on the basis of his fundamental works in operator algebras. It is now a very active branch of mathematics with actual and potential applications to a variety of domains in physics ranging from solid state to quantization of gravity. The strategy is to formulate usual differential geometry in a somewhat unusual manner, using in particular operator algebras and related concepts, so as to be able to plug in noncommutativity in a natural way. Algebraic tools such as K-theory and cyclic cohomology and homology play an important role in this field. It is an important topic both for mathematics and physics.

Advances In Noncommutative Geometry

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Author : Ali Chamseddine
language : en
Publisher: Springer Nature
Release Date : 2020-01-13

Advances In Noncommutative Geometry written by Ali Chamseddine and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-13 with Mathematics categories.

This authoritative volume in honor of Alain Connes, the foremost architect of Noncommutative Geometry, presents the state-of-the art in the subject. The book features an amalgam of invited survey and research papers that will no doubt be accessed, read, and referred to, for several decades to come. The pertinence and potency of new concepts and methods are concretely illustrated in each contribution. Much of the content is a direct outgrowth of the Noncommutative Geometry conference, held March 23–April 7, 2017, in Shanghai, China. The conference covered the latest research and future areas of potential exploration surrounding topology and physics, number theory, as well as index theory and its ramifications in geometry.

Cyclic Cohomology At 40 Achievements And Future Prospects

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Author : A. Connes
language : en
Publisher: American Mathematical Society
Release Date : 2023-02-23

Cyclic Cohomology At 40 Achievements And Future Prospects written by A. Connes 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 2023-02-23 with Mathematics categories.

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.