Infinitesimal Rigidity for Cubulated Manifolds

DOI10.1007/S10711-022-00765-9arXiv2112.10696MaRDI QIDQ6386219

Ludovico Battista

Publication date: 20 December 2021

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 arXiv:2009.04997 [math.GT] and arXiv:2105.14795 [math.GT]. The 5-dimensional example is diffeomorphic to $NimesmathbbR$ 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.

Mathematics Subject Classification ID

General geometric structures on low-dimensional manifolds (57M50) Fundamental group, presentations, free differential calculus (57M05) General topology of 4-manifolds (57K40) Low-dimensional manifolds of specific dimension 5 or higher (57K50)

This page was built for publication: Infinitesimal Rigidity for Cubulated Manifolds

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6386219)