Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds

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Brand new. We distribute directly for the publisher. 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 theory of spectral invariants on closed manifolds and manifolds with 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 traces, indices, and determinants. Part III is concerned with general 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. Read more Show Less

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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: 1/5/2005
  • 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 theory 3
Euclidean quantum gravity in light of spectral geometry 23
Analysis of invariants associated with spectral boundary problems for elliptic operators 43
A resolvent approach to traces and zeta Laurent expansions 76
Asymptotic expansion of the zeta-determinant of an invertible Laplacian on a stretched manifold 95
Agranovich-Dynin formula for the zeta-determinants of the Neumann and Dirichlet problems 109
The Calderon projector for the odd signature operator and spectral flow calculations in 3-dimensional topology 125
Cut-and-paste on foliated bundles 151
The uniqueness of the spectral flow on spaces of unbounded self-adjoint Fredholm operators 193
Variants of equivariant Seiberg-Witten Floer homology 225
Dirac operators, boundary value problems, and the b-calculus 241
Guillemin transform and Toeplitz representations for operators on singular manifolds 281
Pseudodifferential operators on non-compact manifolds and analysis on polyhedral domains 307
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