Strict hyperbolization of flat manifolds

Abstract: Charney–Davis strict hyperbolization is a construction that takes a nonpositively curved cube complex and converts it into a negatively curved space. In this talk, I’ll explain how strict hyperbolization can be used to produce closed hyperbolic manifolds with interesting topological features, by applying it to a suitable class of flat manifolds. This leads to new examples of closed hyperbolic manifolds with nontrivial Pontryagin and Stiefel–Whitney classes, hyperbolic manifolds that arise as totally geodesic boundaries of other hyperbolic manifolds, and aspherical topological manifolds that admit no smooth structure. This is joint work with Eduardo Reyes and Stefano Riolo.

algebraic geometryanalysis of PDEsalgebraic topologycomplex variablesdifferential geometrygeneral topologygeometric topologyK-theory and homologymetric geometrysymplectic geometry

Audience: researchers in the topic

CRM - Séminaire du CIRGET / Géométrie et Topologie

Series comments: Hybrid seminar of geometry and topology. Laboratory : CIRGET - www.cirget.uqam.ca The homepage of the seminar is www.cirget.uqam.ca/fr/seminaires.html

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