L^2-Betti numbers of branched covers of hyperbolic manifolds

TL;DR

This paper demonstrates that Gromov-Thurston branched covers of hyperbolic manifolds satisfy the Singer conjecture under certain prime divisibility conditions related to the base manifold and branch locus.

Contribution

It establishes a new class of hyperbolic branched covers that fulfill the Singer conjecture, linking algebraic properties to geometric topology.

Findings

Gromov-Thurston branched covers satisfy the Singer conjecture under specific prime conditions.

The degree of the cover influences the validity of the Singer conjecture.

Prime divisibility constraints are crucial for the conjecture's applicability.

Abstract

We show that Gromov-Thurston branched covers satisfy the Singer conjecture whenever the degree of the cover is not divisible by a finite set of primes determined by the base manifold and the branch locus.