Resolvent, heat kernel, and torsion under degeneration to fibered cusps

Pierre Albin, Frédéric Rochon, David Sher

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1-138
Number of pages138
JournalMemoirs of the American Mathematical Society
Volume269
Issue number1314
DOIs
StatePublished - Jan 2021

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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