Resolvent, Heat Kernel, and Torsion under Degeneration to Fibered Cusps

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by Pierre Albin, Frederic Rochon
English | 2021 | ISBN: 1470444224 | 138 Pages | True PDF | 1.24 MB

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.


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