Resolvent, heat kernel, and torsion under degeneration to fibered cusps / Pierre Albin, Frédéric Rochon, David Sher.

Format:

Book

Author/Creator:

Albin, Pierre, 1976- author.

Rochon, Frédéric, 1978- author.

Sher, David (David A.), 1987- author.

Series:

Memoirs of the American Mathematical Society ; v. 1314.

Memoirs of the American Mathematical Society, 1947-6221 ; v. 1314

Language:

English

Subjects (All):

Riemannian manifolds.

Symmetric spaces.

Torsion theory (Algebra).

Resolvents (Mathematics).

Heat equation.

Kernel functions.

Surfaces, Algebraic--Degenerations.

Surfaces, Algebraic.

Surgery (Topology).

Physical Description:

1 online resource (pages cm.)

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2021]

System Details:

Mode of access : World Wide Web

text file

Summary:

"Manifolds with fibered cusps are a class of complete non-compact Riemannian manifolds including many examples of locally symmetric spaces of rank one. We study the spectrum of the Hodge Laplacian with coefficients in a flat bundle on a closed manifold undergoing degeneration to a manifold with fibered cusps. We obtain precise asymptotics for the resolvent, the heat kernel, and the determinant of the Laplacian. Using these asymptotics we obtain a topological description of the analytic torsion on a manifold with fibered cusps in terms of the R-torsion of the underlying manifold with boundary"-- Provided by publisher.

Contents:

1. Introduction 2. Fibered cusp surgery metrics Resolvent under degeneration 3. Pseudodifferential operator calculi 4. Resolvent construction 5. Projection onto the eigenspace of small eigenvalues Heat kernel under degeneration 6. Surgery heat space 7. Solving the heat equation Torsion under degeneration 8. The $R$-torsion on manifolds with boundary 9. The intersection $R$-torsion of Dar and $L^2$-cohomology 10. Analytic torsion conventions 11. Asymptotics of analytic torsion 12. A Cheeger-Müller theorem for fibered cusp manifolds A. Model cases: Euclidean Laplacians and Dirac operators B. Geometric microlocal preliminaries C. Proof of composition formula

Notes:

"January 2021, volume 269, number 1314 (fifth of 7 numbers)."

Includes bibliographical references.

Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2021

Description based on print version record.

Other Format:

Print version: Albin, Pierre, 1976- Resolvent, heat kernel, and torsion under degeneration to fibered cusps /

ISBN:

9781470464660

Access Restriction:

Restricted for use by site license.