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Analytic torsion and R-torsion of Witt representations on manifolds with cusps. (English) Zbl 1408.58025
Authors’ abstract: We established a Cheeger-Müller theorem for unimodular representations satisfying a Witt condition on a noncompact manifold with cusps. This class of spaces includes all noncompact hyperbolic spaces of finite volume, but we do not assume that the metric has constant curvature nor that the link of the cusp is a torus. We use renormalized traces in the sense of Melrose to the define Analytic torsion, and we relate it to the intersection \(R\)-torsion of A. Dar [Math. Z. 194, 193–216 (1987; Zbl 0605.57013)] of the natural compactification to a stratified space. Our proof relies on our recent work on the behavior of the Hodge-Laplacian spectrum on a closed manifold undergoing degeneration to a manifold with fibered cusps [the authors, “Resolvent, heat kernel and torsion under degeneration to fibered cusps”, Preprint, arXiv:1410.8406v4].

MSC:
58J52 Determinants and determinant bundles, analytic torsion
58J50 Spectral problems; spectral geometry; scattering theory on manifolds
58J35 Heat and other parabolic equation methods for PDEs on manifolds
55N25 Homology with local coefficients, equivariant cohomology
55N33 Intersection homology and cohomology in algebraic topology
Citations:
Zbl 0605.57013
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