Contemporary Mathematics 2005; 328 pp; softcover Volume: 366 ISBN10: 082183536X ISBN13: 9780821835364 List Price: US$103 Member Price: US$82.40 Order Code: CONM/366
 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. Readership Graduate students and research mathematicians interested in spectral problems in geometry. Table of Contents Part I. Basic materialReviews  D. V. Vassilevich  Spectral problems from quantum field theory
 G. Esposito  Euclidean quantum gravity in light of spectral geometry
 G. Grubb  Analysis of invariants associated with spectral boundary problems for elliptic operators
Part II. Spectral invariants and asymptotic expansions  G. Grubb  A resolvent approach to traces and zeta Laurent expansions
 Y. Lee  Asymptotic expansion of the zetadeterminant of an invertible Laplacian on a stretched manifold
 J. Park and K. P. Wojciechowski  AgranovichDynin formula for the zetadeterminants of the Neumann and Dirichlet problems
Part III. Geometric and topological problems  H. U. Boden, C. M. Herald, and P. Kirk  The Calderón projector for the odd signature operator and spectral flow calculations in 3dimensional topology
 E. Leichtnam and P. Piazza  Cutandpaste on foliated bundles
 M. Lesch  The uniqueness of the spectral flow on spaces of unbounded selfadjoint Fredholm operators
 M. Marcolli and B.L. Wang  Variants of equivariant SeibergWitten Floer homology
Part IV. Manifolds with singularities  P. Loya  Dirac operators, boundary value problems, and the \(b\)calculus
 V. E. Nazaikinskii, G. Rozenblum, A. Yu. Savin, and B. Yu. Sternin  Guillemin transform and Toeplitz representations for operators on singular manifolds
 V. Nistor  Pseudodifferential operators on noncompact manifolds and analysis on polyhedral domains
