Homology growth, hyperbolization, and fibering

2023/01/15 by Grigori Avramidi, Boris Okun, Avramidi, Grigori +3
Computer Science · Mathematics · #20F65 (Primary) 57M07 (Secondary) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2301.06112

openalex publication_date 2023/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 -- \mathbbF_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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