Homology Growth, Hyperbolization, and Fibering

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 — -homology growth above the middle dimension. We use this trick, embedding theory and manifold topology to cons...

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Published inGeometric and functional analysis Vol. 34; no. 2; pp. 303 - 376
Main Authors Avramidi, Grigori, Okun, Boris, Schreve, Kevin
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.04.2024
Springer Nature B.V
Subjects
Analysis
Homology
Manifolds (mathematics)
Mathematics
Mathematics and Statistics
Topology
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Summary: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 — -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.
Bibliography:ObjectType-Article-1
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ISSN:1016-443X
1420-8970
DOI:10.1007/s00039-024-00667-w