Resolvent Heat Kernel And Torsion Under Degeneration To Fibered Cusps
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Resolvent, Heat Kernel, and Torsion under Degeneration to Fibered Cusps
Author: Pierre Albin
language: en
Publisher: American Mathematical Soc.
Release Date: 2021-06-21
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.
Resolvent, Heat Kernel, and Torsion Under Degeneration to Fibered Cusps
Fibered cusp surgery metrics -- Pseudodifferential operator calculi -- Resolvent construction -- Projection onto the eigenspace of small eigenvalues -- Surgery heat space -- Solving the heat equation -- The R-torsion on manifolds with boundary -- The intersection R-torsion of Dar and L2-cohomology -- Analytic torsion conventions -- Asymptotics of analytic torsion -- A Cheeger-Muller theorem for fibered cusp manifolds.
The Yang-Mills Heat Equation with Finite Action in Three Dimensions
Author: Leonard Gross
language: en
Publisher: American Mathematical Society
Release Date: 2022-02-02
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