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Author: Wolfgang Lück
Publisher: Springer Science & Business Media
ISBN: 3662046873
Category : Mathematics
Languages : en
Pages : 604
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Book Description
In algebraic topology some classical invariants - such as Betti numbers and Reidemeister torsion - are defined for compact spaces and finite group actions. They can be generalized using von Neumann algebras and their traces, and applied also to non-compact spaces and infinite groups. These new L2-invariants contain very interesting and novel information and can be applied to problems arising in topology, K-Theory, differential geometry, non-commutative geometry and spectral theory. The book, written in an accessible manner, presents a comprehensive introduction to this area of research, as well as its most recent results and developments.
Author: Wolfgang Lück
Publisher: Springer Science & Business Media
ISBN: 3662046873
Category : Mathematics
Languages : en
Pages : 604
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Book Description
In algebraic topology some classical invariants - such as Betti numbers and Reidemeister torsion - are defined for compact spaces and finite group actions. They can be generalized using von Neumann algebras and their traces, and applied also to non-compact spaces and infinite groups. These new L2-invariants contain very interesting and novel information and can be applied to problems arising in topology, K-Theory, differential geometry, non-commutative geometry and spectral theory. The book, written in an accessible manner, presents a comprehensive introduction to this area of research, as well as its most recent results and developments.
Author: Liviu I. Nicolaescu
Publisher: Walter de Gruyter
ISBN: 311019810X
Category : Mathematics
Languages : en
Pages : 264
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Book Description
This is a state-of-the-art introduction to the work of Franz Reidemeister, Meng Taubes, Turaev, and the author on the concept of torsion and its generalizations. Torsion is the oldest topological (but not with respect to homotopy) invariant that in its almost eight decades of existence has been at the center of many important and surprising discoveries. During the past decade, in the work of Vladimir Turaev, new points of view have emerged, which turned out to be the "right ones" as far as gauge theory is concerned. The book features mostly the new aspects of this venerable concept. The theoretical foundations of this subject are presented in a style accessible to those, who wish to learn and understand the main ideas of the theory. Particular emphasis is upon the many and rather diverse concrete examples and techniques which capture the subleties of the theory better than any abstract general result. Many of these examples and techniques never appeared in print before, and their choice is often justified by ongoing current research on the topology of surface singularities. The text is addressed to mathematicians with geometric interests who want to become comfortable users of this versatile invariant.
Author: Bernhelm Booss
Publisher: World Scientific
ISBN: 9812568050
Category : Science
Languages : en
Pages : 553
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Book Description
Modern theory of elliptic operators, or simply elliptic theory, has been shaped by the Atiyah-Singer Index Theorem created 40 years ago. Reviewing elliptic theory over a broad range, 32 leading scientists from 14 different countries present recent developments in topology; heat kernel techniques; spectral invariants and cutting and pasting; noncommutative geometry; and theoretical particle, string and membrane physics, and Hamiltonian dynamics.The first of its kind, this volume is ideally suited to graduate students and researchers interested in careful expositions of newly-evolved achievements and perspectives in elliptic theory. The contributions are based on lectures presented at a workshop acknowledging Krzysztof P Wojciechowski's work in the theory of elliptic operators.
Author: Matthias Lesch
Publisher: World Scientific
ISBN: 9814478024
Category : Mathematics
Languages : en
Pages : 553
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Book Description
Modern theory of elliptic operators, or simply elliptic theory, has been shaped by the Atiyah-Singer Index Theorem created 40 years ago. Reviewing elliptic theory over a broad range, 32 leading scientists from 14 different countries present recent developments in topology; heat kernel techniques; spectral invariants and cutting and pasting; noncommutative geometry; and theoretical particle, string and membrane physics, and Hamiltonian dynamics.The first of its kind, this volume is ideally suited to graduate students and researchers interested in careful expositions of newly-evolved achievements and perspectives in elliptic theory. The contributions are based on lectures presented at a workshop acknowledging Krzysztof P Wojciechowski's work in the theory of elliptic operators.
Author: Motoko Kotani
Publisher: American Mathematical Soc.
ISBN: 0821842692
Category : Mathematics
Languages : en
Pages : 363
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Book Description
This volume is an outgrowth of an international conference in honor of Toshikazu Sunada on the occasion of his sixtieth birthday. The conference took place at Nagoya University, Japan, in 2007. Sunada's research covers a wide spectrum of spectral analysis, including interactions among geometry, number theory, dynamical systems, probability theory and mathematical physics. Readers will find papers on trace formulae, isospectral problems, zeta functions, quantum ergodicity, random waves, discrete geometric analysis, value distribution, and semiclassical analysis. This volume also contains an article that presents an overview of Sunada's work in mathematics up to the age of sixty.
Author: I.M. Gelfand
Publisher: Springer Science & Business Media
ISBN: 1461240824
Category : Mathematics
Languages : en
Pages : 278
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Book Description
The Seminar has taken place at Rutgers University in New Brunswick, New Jersey, since 1990 and it has become a tradition, starting in 1992, that the Seminar be held during July at IHES in Bures-sur-Yvette, France. This is the second Gelfand Seminar volume published by Birkhauser, the first having covered the years 1990-1992. Most of the papers in this volume result from Seminar talks at Rutgers, and some from talks at IHES. In the case of a few of the papers the authors did not attend, but the papers are in the spirit of the Seminar. This is true in particular of V. Arnold's paper. He has been connected with the Seminar for so many years that his paper is very natural in this volume, and we are happy to have it included here. We hope that many people will find something of interest to them in the special diversity of topics and the uniqueness of spirit represented here. The publication of this volume would be impossible without the devoted attention of Ann Kostant. We are extremely grateful to her. I. Gelfand J. Lepowsky M. Smirnov Questions and Answers About Geometric Evolution Processes and Crystal Growth Fred Almgren We discuss evolutions of solids driven by boundary curvatures and crystal growth with Gibbs-Thomson curvature effects. Geometric measure theo retic techniques apply both to smooth elliptic surface energies and to non differentiable crystalline surface energies.
Author: Gerald W. Johnson
Publisher: Clarendon Press
ISBN: 0191546267
Category : Mathematics
Languages : en
Pages : 790
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Book Description
This book provides the most comprehensive mathematical treatment to date of the Feynman path integral and Feynman's operational calculus. It is accessible to mathematicians, mathematical physicists and theoretical physicists. Including new results and much material previously only available in the research literature, this book discusses both the mathematics and physics background that motivate the study of the Feynman path integral and Feynman's operational calculus, and also provides more detailed proofs of the central results.
Author: Melvin Rothenberg
Publisher: American Mathematical Soc.
ISBN: 0821813625
Category : Mathematics
Languages : en
Pages : 334
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Book Description
This volume presents the proceedings of the Tel Aviv International Topology Conference held during the Special Topology Program at Tel Aviv University. The book is dedicated to Professor Mel Rothenberg on the occasion of his 65th birthday. His contributions to topology are well known-from the early work on triangulations to numerous papers on transformation groups and on geometric and analytic aspects of torsion theory. Current research related to those contributions are reported in this book. Coverage is included on the following topics: vanishing theorems for the Dirac operator, the theory of Reidemeister torsion (including infinite dimensional flat bundles), Nobikov-Shubin invariants of manifolds, topology of group actions, Lusternik-Schnirelman theory for closed 1-forms, finite type invariants of links and 3-manifolds, equivariant cobordisms, equivariant orientations and Thom isomorphisms, and more.
Author: Piotr Kielanowski
Publisher: Birkhäuser
ISBN: 3319182129
Category : Mathematics
Languages : en
Pages : 322
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Book Description
This book presents a selection of papers based on the XXXIII Białowieża Workshop on Geometric Methods in Physics, 2014. The Białowieża Workshops are among the most important meetings in the field and attract researchers from both mathematics and physics. The articles gathered here are mathematically rigorous and have important physical implications, addressing the application of geometry in classical and quantum physics. Despite their long tradition, the workshops remain at the cutting edge of ongoing research. For the last several years, each Białowieża Workshop has been followed by a School on Geometry and Physics, where advanced lectures for graduate students and young researchers are presented; some of the lectures are reproduced here. The unique atmosphere of the workshop and school is enhanced by its venue, framed by the natural beauty of the Białowieża forest in eastern Poland. The volume will be of interest to researchers and graduate students in mathematical physics, theoretical physics and mathematmtics.
Author: Jerzy Jezierski
Publisher:
ISBN:
Category : Fixed point theory
Languages : en
Pages : 276
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Book Description
