2021
DOI: 10.1017/etds.2021.91
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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 $\mathrm{PU}(m,1)$ -cocycles of complex hyperbolic lattices.

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Cited by 3 publications
(4 citation statements)
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“…Clearly, the natural volume of a cocycle will be invariant by the conjugation action of G(m) on the space of cocycles. Moreover, this volume satisfies a Milnor-Wood inequality type similar to the one obtained by Bucher, Burger and Iozzi [12] for representations, by Bader, Furman and Sauer [4] for self-couplings and by the author and Moraschini [36,37] for cocycles. Notice that the result obtained in [36] is valid for n = m, whereas here we can also consider the case m > n.…”
Section: A Savinisupporting
confidence: 68%
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“…Clearly, the natural volume of a cocycle will be invariant by the conjugation action of G(m) on the space of cocycles. Moreover, this volume satisfies a Milnor-Wood inequality type similar to the one obtained by Bucher, Burger and Iozzi [12] for representations, by Bader, Furman and Sauer [4] for self-couplings and by the author and Moraschini [36,37] for cocycles. Notice that the result obtained in [36] is valid for n = m, whereas here we can also consider the case m > n.…”
Section: A Savinisupporting
confidence: 68%
“…As already discussed in the Introduction, even if we are going to focus our attention only on uniform lattices, the same results of the section will hold also in the nonuniform case. Notice also that the definition we are going to give differs from the one given in [36, 37] since ours relies on the differentiability of the slices of essentially bounded equivariant maps (see Definition 4.1). Moreover, the rigidity result we are going to obtain will refer to cocycles associated to lattices of with image into , with m possibly greater than or equal to n .…”
Section: Natural Volume Of Zimmer Cocyclesmentioning
confidence: 99%
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“…for every γ ∈ Γ and almost every ξ ∈ ∂ ∞ H n C , s ∈ Ω. This means exactly that φ is a boundary map in the sense of [MS,Definition 2.9]. If we now show that the slice…”
Section: Superrigidity For Complex Cocyclesmentioning
confidence: 89%