Spectral Asymmetry and Index Theory on Manifolds with Generalised Hyperbolic Cusps

On the spectral theory and dynamics of asymptotically hyperbolic manifolds

— We present a brief survey of the spectral theory and dynamics of infinite volume asymptotically hyperbolic manifolds. Beginning with their geometry and examples, we proceed to their spectral and scattering theories, dynamics, and the physical description of their quantum and classical mechanics. We conclude with a discussion of recent results, ideas, and conjectures. Résumé. — Cet article est...

Spectral theory of the p-form Laplacian on manifolds with generalized cusps

Spectral theory and scattering theory on non-compact manifolds with ends of various shapes have had a huge influence on mathematics and physics. One important and extensively studied family consists of manifolds with hyperbolic cusps. These manifolds first appeared in mathematics in the context of number theory as quotients of the upper half plane by arithmetic lattices. It was discovered that ...

Similar Fillings and Isolation of Cusps of Hyperbolic 3-manifolds

In this paper we deepen the analysis of certain classes Mg,k of hyperbolic 3-manifolds that were introduced in a previous work by B. Martelli, C. Petronio and the author. Each element of Mg,k is an oriented complete finite-volume hyperbolic 3manifold with compact connected geodesic boundary of genus g and k cusps. We study small deformations of the complete hyperbolic structure of manifolds in ...

All at Manifolds Are Cusps of Hyperbolic Orbifolds

All flat manifolds are cusps of hyperbolic orbifolds

We show that all closed flat n-manifolds are diffeomorphic to a cusp cross-section in a finite volume hyperbolic n + 1-orbifold.