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 (Battista in Trans Am Math Soc 375(04):2597–2625, 2022; Italiano et al. in Invent Math, 2022. https://doi.org/10.1007/s00222-022-01141-w). The 5-dimensional example is diffeomorphic to 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.

Infinitesimal rigidity for cubulated manifolds

Ludovico Battista
2023-01-01

Abstract

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 (Battista in Trans Am Math Soc 375(04):2597–2625, 2022; Italiano et al. in Invent Math, 2022. https://doi.org/10.1007/s00222-022-01141-w). The 5-dimensional example is diffeomorphic to 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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11582/346730
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