Homology growth, hyperbolization, and fibering

Grigori Avramidi; Boris Okun; Kevin Schreve

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arXiv · 2301.06112

Homology growth, hyperbolization, and fibering

Grigori Avramidi·Boris Okun·Kevin Schreve

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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.

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Grigori Avramidi, Boris Okun, Kevin Schreve. 2023-01-15. Homology growth, hyperbolization, and fibering. https://arxiv.org/abs/2301.06112

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