"January 2021, volume 269, number 1314 (fifth of 7 numbers)." Includes bibliographical references (pages 123-126).
Contents:
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.
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.
Series:
Memoirs of the American Mathematical Society, 0065-9266 ; number 1314
This resource is supported by the Institute of Museum and Library Services under the provisions of the Library Services and Technology Act as administered by State Library of Iowa.