Multiplicative constants and maximal measurable cocycles in bounded cohomology

Abstract

Multiplicative constants are a fundamental tool in the study of maximal representations. In this paper we show how to extend such notion, and the associated framework, to measurable cocycles theory. As an application of this approach, we define and study the Cartan invariant for measurable $\text{PU}(m,1)$-cocycles of complex hyperbolic lattices.

35 pages; Major corrections along the paper following the referee's suggestions. To appear in Ergod. Theory Dyn. Syst

References in corpus (5)

• Non-ergodic actions, cocycles and superrigidity
• Superrigidity of maximal measurable cocycles of complex hyperbolic lattices
• Stable integral simplicial volume of 3-manifolds
• Natural maps for measurable cocycles of compact hyperbolic manifolds
• Integrable tautness of isometries of complex hyperbolic spaces

Cited by in corpus (2)

• Superrigidity of maximal measurable cocycles of complex hyperbolic lattices
• Natural maps for measurable cocycles of compact hyperbolic manifolds