Homology Growth, Hyperbolization, and Fibering

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2024年2月14日

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Grigori Avramidi,
Boris Okun,
Kevin Schreve

摘要

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.