Homology growth, hyperbolization, and fibering

Abstract

We introduce a hyperbolic reflection group trick which builds closed aspherical manifolds out of compact ones and preserves hyperbolicity, residual finiteness, and -- for almost all primes $p$ -- ${\mathbb{F}}_p$-homology growth above the middle dimension. We use this trick, embedding theory and manifold topology to construct Gromov hyperbolic $7$-manifolds that do not virtually fiber over a circle out of graph products of large finite groups.

Fixed a gap in Section 10, added Theorem 5.4, numerous small fixes and changes