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Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds
 
Edited by: Bernhelm Booß-Bavnbek :  Roskilde University, Roskilde, Denmark
Gerd Grubb :  University of Copenhagen, Copenhagen, Denmark
Krzysztof P. Wojciechowski :  Indiana University–Purdue University, Indianapolis, IN
Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds
eBook ISBN:  978-0-8218-7956-6
Product Code:  CONM/366.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Add to cart
Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds
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Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds
Edited by: Bernhelm Booß-Bavnbek :  Roskilde University, Roskilde, Denmark
Gerd Grubb :  University of Copenhagen, Copenhagen, Denmark
Krzysztof P. Wojciechowski :  Indiana University–Purdue University, Indianapolis, IN
eBook ISBN:  978-0-8218-7956-6
Product Code:  CONM/366.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Add to cart
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 366; 2005; 328 pp
    MSC: Primary 19; 35; 46; 47; 58; 81; 83

    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 Material—Reviews [ MR 2114480 ]
    • 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 ]
    • Part II. Spectral Invariants and Asymptotic Expansions [ MR 2114480 ]
    • 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 ]
    • Part III. Geometric and Topological Problems [ MR 2114480 ]
    • 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 ]
    • Part IV. Manifolds with Singularities [ MR 2114480 ]
    • 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 ]
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Contemporary Mathematics
Volume: 366; 2005; 328 pp
MSC: Primary 19; 35; 46; 47; 58; 81; 83

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.
  • Part I. Basic Material—Reviews [ MR 2114480 ]
  • 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 ]
  • Part II. Spectral Invariants and Asymptotic Expansions [ MR 2114480 ]
  • 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 ]
  • Part III. Geometric and Topological Problems [ MR 2114480 ]
  • 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 ]
  • Part IV. Manifolds with Singularities [ MR 2114480 ]
  • 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 ]
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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