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"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"--

Riemannian manifolds. --- Symmetric spaces. --- Torsion theory (Algebra) --- Riemann, Variétés de --- Espaces symétriques --- Torsion, Théorie de la (algèbre) --- Resolvents (Mathematics) --- Heat equation. --- Kernel functions. --- Surfaces, Algebraic --- Surgery (Topology) --- Degenerations.

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Algebraic topology --- H-spaces --- Obstruction theory --- Torsion theory (Algebra) --- Commutative rings --- Ideals (Algebra) --- Modules (Algebra) --- Hopf spaces --- Spaces, Hopf --- Topological groups --- H-spaces. --- Obstruction theory. --- Torsion, Théorie de la (algèbre) --- Obstructions, Théorie des. --- H-espaces.

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Complex analysis --- Functions, Theta --- Kernel functions --- Moduli theory --- Theory of moduli --- Analytic spaces --- Functions of several complex variables --- Geometry, Algebraic --- Functions, Kernel --- Functions of complex variables --- Geometric function theory --- Theta functions --- Kernel functions. --- Torsion theory (Algebra) --- Torsion, Théorie de la (algèbre) --- Modules, Théorie des --- Bergman, Noyaux de --- Fonctions thêta --- Modules, Théorie des. --- Bergman, Noyaux de. --- Fonctions thêta.