Collisions at infinity in hyperbolic manifolds

TL;DR

This paper studies the relationship between the homology of cusps and the entire hyperbolic manifold, providing a key proof needed for recent research in the field.

Contribution

It offers a new proof of a crucial result linking cusp homology to the manifold's homology in hyperbolic geometry.

Findings

Established a map between cusp homology and manifold homology

Provided a proof supporting recent theoretical developments

Clarified the structure of homology at infinity in hyperbolic manifolds

Abstract

For a complete, finite volume real hyperbolic n-manifold M, we investigate the map between homology of the cusps of M and the homology of $M$. Our main result provides a proof of a result required in a recent paper of Frigerio, Lafont, and Sisto.