arXiv
Open Access
2021
Infinitesimal Rigidity for Cubulated Manifolds
Ludovico Battista
Abstrak
We prove the infinitesimal rigidity of some geometrically infinite hyperbolic 4- and 5-manifolds. These examples arise as infinite cyclic coverings of finite-volume hyperbolic manifolds obtained by colouring right-angled polytopes, already described in the papers arXiv:2009.04997 [math.GT] and arXiv:2105.14795 [math.GT]. The 5-dimensional example is diffeomorphic to $N \times \mathbb{R}$ for some aspherical 4-manifold $N$ which does not admit any hyperbolic structure. To this purpose we develop a general strategy to study the infinitesimal rigidity of cyclic coverings of manifolds obtained by colouring right-angled polytopes.
Topik & Kata Kunci
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Ludovico Battista
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2021
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- arXiv
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- Open Access ✓