Multiplicative constants and maximal measurable cocycles in bounded cohomology

TL;DR

This paper extends the concept of multiplicative constants to measurable cocycles, enabling the definition and analysis of the Cartan invariant for measurable PU(m,1)-cocycles in complex hyperbolic lattices.

Contribution

It introduces a new framework for multiplicative constants in measurable cocycles and applies it to define the Cartan invariant in this context.

Findings

Extended multiplicative constants framework to measurable cocycles

Defined the Cartan invariant for PU(m,1)-cocycles

Analyzed properties of the Cartan invariant in complex hyperbolic lattices

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 $\textup{PU}(m,1)$-cocycles of complex hyperbolic lattices.