Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds
About this Title
Bernhelm Booß-Bavnbek, Gerd Grubb and Krzysztof P. Wojciechowski, Editors
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.
Graduate students and research mathematicians interested in spectral problems in geometry.
Table of Contents
- Dmitri V. Vassilevich – Spectral problems from quantum field theory [MR 2114481]
- Giampiero Esposito – Euclidean quantum gravity in light of spectral geometry [MR 2114482]
- Gerd Grubb – Analysis of invariants associated with spectral boundary problems for elliptic operators [MR 2114483]
- Gerd Grubb – A resolvent approach to traces and zeta Laurent expansions [MR 2114484]
- Yoonweon Lee – Asymptotic expansion of the zeta-determinant of an invertible Laplacian on a stretched manifold [MR 2114485]
- Jinsung Park and Krzysztof P. Wojciechowski – Agranovich-Dynin formula for the zeta-determinants of the Neumann and Dirichlet problems [MR 2114486]
- Hans U. Boden, Christopher M. Herald and Paul Kirk – The Calderón projector for the odd signature operator and spectral flow calculations in 3-dimensional topology [MR 2114487]
- Eric Leichtnam and Paolo Piazza – Cut-and-paste on foliated bundles [MR 2114488]
- Matthias Lesch – The uniqueness of the spectral flow on spaces of unbounded self-adjoint Fredholm operators [MR 2114489]
- Matilde Marcolli and Bai-Ling Wang – Variants of equivariant Seiberg-Witten Floer homology [MR 2114490]
- Paul Loya – Dirac operators, boundary value problems, and the $b$-calculus [MR 2114491]
- V. E. Nazaikinskii, G. Rozenblum, A. Yu. Savin and B. Yu. Sternin – Guillemin transform and Toeplitz representations for operators on singular manifolds [MR 2114492]
- Victor Nistor – Pseudodifferential operators on non-compact manifolds and analysis on polyhedral domains [MR 2114493]