Geometric And Topological Invariants Of Elliptic Operators
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Author | : Jerome Kaminker |
Publisher | : American Mathematical Soc. |
Total Pages | : 312 |
Release | : 1990 |
Genre | : Mathematics |
ISBN | : 0821851128 |
Download Geometric and Topological Invariants of Elliptic Operators Book in PDF, Epub and Kindle
This volume contains the proceedings of the AMS-IMS-SIAM Summer Research Conference on ``Geometric and Topological Invariants of Elliptic Operators,'' held in August 1988 at Bowdoin College. Some of the themes covered at the conference and appearing in the articles are: the use of more sophisticated asymptotic methods to obtain index theorems, the study of the $\eta$ invariant and analytic torsion, and index theory on open manifolds and foliated manifolds. The current state of noncommutative differential geometry, as well as operator algebraic and $K$-theoretic methods, are also presented in several the articles. This book will be useful to researchers in index theory, operator algebras, foliations, and mathematical physics. Topologists and geometers are also likely to find useful the view the book provides of recent work in this area. In addition, because of the expository nature of several of the articles, it will be useful to graduate students interested in working in these areas.
Author | : Vladimir E. Nazaykinskiy |
Publisher | : Springer Science & Business Media |
Total Pages | : 224 |
Release | : 2008-06-30 |
Genre | : Mathematics |
ISBN | : 3764387750 |
Download Elliptic Theory and Noncommutative Geometry Book in PDF, Epub and Kindle
This comprehensive yet concise book deals with nonlocal elliptic differential operators. These are operators whose coefficients involve shifts generated by diffeomorphisms of the manifold on which the operators are defined. This is the first book featuring a consistent application of methods of noncommutative geometry to the index problem in the theory of nonlocal elliptic operators. To make the book self-contained, the authors have included necessary geometric material.
Author | : Bernhelm Booss |
Publisher | : World Scientific |
Total Pages | : 553 |
Release | : 2006 |
Genre | : Science |
ISBN | : 9812568050 |
Download Analysis, Geometry and Topology of Elliptic Operators Book in PDF, Epub and Kindle
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 | : |
Publisher | : |
Total Pages | : 297 |
Release | : 1990 |
Genre | : |
ISBN | : |
Download Geometric and Topological Invariants of Elliptic Operators Book in PDF, Epub and Kindle
Author | : Matthias Lesch |
Publisher | : World Scientific |
Total Pages | : 553 |
Release | : 2006-04-25 |
Genre | : Mathematics |
ISBN | : 9814478024 |
Download Analysis, Geometry And Topology Of Elliptic Operators: Papers In Honor Of Krzysztof P Wojciechowski Book in PDF, Epub and Kindle
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 | : John Roe |
Publisher | : CRC Press |
Total Pages | : 218 |
Release | : 2013-12-19 |
Genre | : Mathematics |
ISBN | : 1482247836 |
Download Elliptic Operators, Topology, and Asymptotic Methods Book in PDF, Epub and Kindle
Ten years after publication of the popular first edition of this volume, the index theorem continues to stand as a central result of modern mathematics-one of the most important foci for the interaction of topology, geometry, and analysis. Retaining its concise presentation but offering streamlined analyses and expanded coverage of important exampl
Author | : M.F. Atiyah |
Publisher | : Springer |
Total Pages | : 100 |
Release | : 2006-08-01 |
Genre | : Mathematics |
ISBN | : 3540378111 |
Download Elliptic Operators and Compact Groups Book in PDF, Epub and Kindle
Author | : Jerome Kaminker |
Publisher | : American Mathematical Soc. |
Total Pages | : 334 |
Release | : 1988 |
Genre | : Mathematics |
ISBN | : 0821850776 |
Download Index Theory of Elliptic Operators, Foliations, and Operator Algebras Book in PDF, Epub and Kindle
Combining analysis, geometry, and topology, this volume provides an introduction to current ideas involving the application of $K$-theory of operator algebras to index theory and geometry. In particular, the articles follow two main themes: the use of operator algebras to reflect properties of geometric objects and the application of index theory in settings where the relevant elliptic operators are invertible modulo a $C^*$-algebra other than that of the compact operators. The papers in this collection are the proceedings of the special sessions held at two AMS meetings: the Annual meeting in New Orleans in January 1986, and the Central Section meeting in April 1986. Jonathan Rosenberg's exposition supplies the best available introduction to Kasparov's $KK$-theory and its applications to representation theory and geometry. A striking application of these ideas is found in Thierry Fack's paper, which provides a complete and detailed proof of the Novikov Conjecture for fundamental groups of manifolds of non-positive curvature. Some of the papers involve Connes' foliation algebra and its $K$-theory, while others examine $C^*$-algebras associated to groups and group actions on spaces.
Author | : Gerd Grubb |
Publisher | : American Mathematical Soc. |
Total Pages | : 338 |
Release | : 2005 |
Genre | : Mathematics |
ISBN | : 082183536X |
Download Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds Book in PDF, Epub and Kindle
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.
Author | : IUrii Petrovich Solov'ev |
Publisher | : American Mathematical Soc. |
Total Pages | : 213 |
Release | : 2001 |
Genre | : Mathematics |
ISBN | : 9780821813997 |
Download C*-algebras and Elliptic Operators in Differential Topology Book in PDF, Epub and Kindle
The aim of this book is to present some applications of functional analysis and the theory of differential operators to the investigation of topological invariants of manifolds. The main topological application discussed in the book concerns the problem of the description of homotopy - invariant rational Pontryagin numbers of non-simply connected manifolds and the Novikov conjecture of homotopy invariance of higher signatures. The definition of higher signatures and the formulation of the Novikov conjecture are given in Chapter 3. In this chapter, the authors also give an overview of different approaches to the proof of the Novikov conjecture. First, there is the Mishchenko symmetric signature and the generalized Hirzebruch formulae and the Mishchenko theorem of homotopy invariance of higher signatures for manifolds whose fundamental groups have a classifying space, being a complete Riemannian non-positive curvature manifold.Then the authors present Solovyov's proof of the Novikov conjecture for manifolds with fundamental group isomorphic to a discrete subgroup of a linear algebraic group over a local field, based on the notion of the Bruhat-Tits building. Finally, the authors discuss the approach due to Kasparov based on the operator $KK$-theory and another proof of the Mishchenko theorem. In Chapter 4, they outline the approach to the Novikov conjecture due to Connes and Moscovici involving cyclic homology.That allows one to prove the conjecture in the case when the fundamental group is a (Gromov) hyperbolic group. The text provides a concise exposition of some topics from functional analysis (for instance, $C^*$-Hilbert modules, $K$-theory or $C^*$-bundles, Hermitian $K$-theory, Fredholm representations, $KK$-theory, and functional integration) from the theory of differential operators (pseudodifferential calculus and Sobolev chains over $C^*$-algebras), and from differential topology (characteristic classes). The book explains basic ideas of the subject and can serve as a course text for an introduction to the study of original works and special monographs.