- Numerical invariants for measurable cocycles
- Sarti, Filippo <1993>
Subject
- MAT/03 Geometria
Description
- The theory of numerical invariants for representations can be generalized to measurable cocycles. This provides a natural notion of maximality for cocycles associated to complex hyperbolic lattices with values in groups of Hermitian type. Among maximal cocycles, the class of Zariski dense ones turns out to have a rigid behavior.
An alternative implementation of numerical invariants can be given by using equivariant maps at the level of boundaries and by exploiting the Burger-Monod approach to bounded cohomology.
Due to their crucial role in this theory, we prove existence results in two different contexts.
Precisely, we construct boundary maps for non-elementary cocycles into the isometry group of CAT(0)-spaces of finite telescopic dimension and for Zariski dense cocycles into simple Lie groups.
Then we approach numerical invariants.
Our first goal is to study cocycles from complex hyperbolic lattices into the Hermitian group SU(p,q).
Following the theory recently developed by Moraschini and Savini, we define the Toledo invariant by using the pullback along cocycles, also by involving boundary maps.
For cocycles Γ × X → SU(p,q) with 1
Date
- 2022-06-20
Type
- Doctoral Thesis
- PeerReviewed
Format
- application/pdf
Identifier
urn:nbn:it:unibo-28783
Sarti, Filippo (2022) Numerical invariants for measurable cocycles, [Dissertation thesis], Alma Mater Studiorum Università di Bologna. Dottorato di ricerca in Matematica