Local rigidity of aspherical three-manifolds

Abstract

International audienc

Exotic Finite Functorial Semi-Norms on Singular Homology

“…For example, in the case that B is a hyperbolic surface and p is a non-trivial bundle, this class was considered by Derbez in the study of local rigidity of aspherical 3-manifolds [2]. More generally, if B is an oriented closed connected hyperbolic manifold, the class α will be nontrivial -it will even have non-zero ℓ 1 -semi-norm.…”

“…Then the induced map [8]. In particular, if M and B are oriented closed connected manifolds of dimension n and n − 1 respectively, we obtain the codimension 1 class 1 -homology of M. For example, in the case that B is a hyperbolic surface and p is a non-trivial bundle, this class was considered by Derbez in the study of local rigidity of aspherical 3-manifolds [2]. More generally, if B is an oriented closed connected hyperbolic manifold, the class α will be nontrivial -it will even have non-zero ℓ 1 -semi-norm.…”

Epimorphisms of 3-manifold groups

“…This result has been generalized in many directions, see e.g. [Som95,Der10,Der12], by using the Gromov simplicial volume [Gr82].…”