Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds

Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds

by Bernhelm Booß-Bavnbek
     
 

ISBN-10: 082183536X

ISBN-13: 9780821835364

Pub. Date: 01/05/2005

Publisher: American Mathematical Society

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

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Overview

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 range from spectral flow calculations and cut-and-paste considerations, via pseudodifferential methods, asymptotic expansions and variational arguments, to singular manifold theories and $K$-theoretic cohomological strategies. They lead to results on determinants, heat kernels, general trace, index and higher signature formulas, low-dimensional topological invariants, as well as on the structure of the manifolds and operators involved. Moreover, the approaches and results are placed in a physics context by two reviews on the applications in quantum field theory, respectively quantum gravity. This book is suitable for graduate students and researchers interested in spectral problems in geometry.

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Product Details

ISBN-13:
9780821835364
Publisher:
American Mathematical Society
Publication date:
01/05/2005
Series:
Contemporary Mathematics Series, #366
Pages:
328
Product dimensions:
67.50(w) x 95.00(h) x 7.50(d)

Table of Contents

Spectral problems from quantum field theory3
Euclidean quantum gravity in light of spectral geometry23
Analysis of invariants associated with spectral boundary problems for elliptic operators43
A resolvent approach to traces and zeta Laurent expansions76
Asymptotic expansion of the zeta-determinant of an invertible Laplacian on a stretched manifold95
Agranovich-Dynin formula for the zeta-determinants of the Neumann and Dirichlet problems109
The Calderon projector for the odd signature operator and spectral flow calculations in 3-dimensional topology125
Cut-and-paste on foliated bundles151
The uniqueness of the spectral flow on spaces of unbounded self-adjoint Fredholm operators193
Variants of equivariant Seiberg-Witten Floer homology225
Dirac operators, boundary value problems, and the b-calculus241
Guillemin transform and Toeplitz representations for operators on singular manifolds281
Pseudodifferential operators on non-compact manifolds and analysis on polyhedral domains307

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