Numerical invariants and volume rigidity for hyperbolic lattices
Savini, Alessio <1990>
Subject
MAT/03 Geometria
Description
We prove a generalization of Mostow-Prasad rigidity by showing that the volume function on the PO(m,1)-character variety of a non-uniform real hyperbolic lattice of PO(p,1) stays away from its maximum outside a suitable analytic neighborhood of the class of the discrete and faithful representation, when m>=p>=3. The same for non-uniform complex and quaternionic hyperbolic lattices for m>=p>=2.
When G is a non-uniform lattice of PSL(2,C) without torsion we define the omega-Borel invariant for representations into SL(n,C_om) and we discuss its properties.
Savini, Alessio (2018) Numerical invariants and volume rigidity for hyperbolic lattices, [Dissertation thesis], Alma Mater Studiorum Università di Bologna. Dottorato di ricerca in Matematica , 30 Ciclo. DOI 10.6092/unibo/amsdottorato/8464.