Stably tangential strict hyperbolization
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911628884180992 |
|---|---|
| author | Bustamante, Mauricio Reyes, Eduardo Riolo, Stefano |
| author_facet | Bustamante, Mauricio Reyes, Eduardo Riolo, Stefano |
| contents | We show that the Charney--Davis strict hyperbolization procedure can preserve stable tangent bundles, answering a question of Charney and Davis. The key input is the construction of many hyperbolizing pieces, obtained using separability properties of hyperbolic cubulable groups. Moreover, these pieces may be chosen so that every face is connected, answering a question of Belegradek. We then apply this construction to suitable cubulations of flat manifolds to produce infinitely many commensurability classes of closed hyperbolic manifolds, both arithmetic and non-arithmetic, with diverse topological features. In particular, we obtain the first examples in which all the Stiefel--Whitney classes are non-trivial below the top degree, and the first orientable examples with non-trivial Pontryagin classes. We also construct infinite towers of finite covers of closed hyperbolic manifolds in which no cover is stably parallelizable or spin. Our methods further yield new pairs of exotic negatively curved Riemannian manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_05956 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stably tangential strict hyperbolization Bustamante, Mauricio Reyes, Eduardo Riolo, Stefano Geometric Topology Group Theory We show that the Charney--Davis strict hyperbolization procedure can preserve stable tangent bundles, answering a question of Charney and Davis. The key input is the construction of many hyperbolizing pieces, obtained using separability properties of hyperbolic cubulable groups. Moreover, these pieces may be chosen so that every face is connected, answering a question of Belegradek. We then apply this construction to suitable cubulations of flat manifolds to produce infinitely many commensurability classes of closed hyperbolic manifolds, both arithmetic and non-arithmetic, with diverse topological features. In particular, we obtain the first examples in which all the Stiefel--Whitney classes are non-trivial below the top degree, and the first orientable examples with non-trivial Pontryagin classes. We also construct infinite towers of finite covers of closed hyperbolic manifolds in which no cover is stably parallelizable or spin. Our methods further yield new pairs of exotic negatively curved Riemannian manifolds. |
| title | Stably tangential strict hyperbolization |
| topic | Geometric Topology Group Theory |
| url | https://arxiv.org/abs/2604.05956 |