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15 November 2018 The bounded Borel class and 3-manifold groups
Michelle Bucher, Marc Burger, Alessandra Iozzi
Duke Math. J. 167(17): 3129-3169 (15 November 2018). DOI: 10.1215/00127094-2018-0038

Abstract

If Γ<PSL(2,C) is a lattice, we define an invariant of a representation ΓPSL(n,C) using the Borel class β(n)Hc3(PSL(n,C),R). We show that this invariant satisfies a Milnor–Wood type inequality and its maximal value is attained precisely by the representations conjugate to the restriction to Γ of the irreducible complex n-dimensional representation of PSL(2,C) or its complex conjugate. Major ingredients of independent interest are the study of our extension to degenerate configurations of flags of a cocycle defined by Goncharov, as well as the identification of Hb3(SL(n,C),R) as a normed space.

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Michelle Bucher. Marc Burger. Alessandra Iozzi. "The bounded Borel class and 3-manifold groups." Duke Math. J. 167 (17) 3129 - 3169, 15 November 2018. https://doi.org/10.1215/00127094-2018-0038

Information

Received: 12 February 2017; Revised: 2 July 2018; Published: 15 November 2018
First available in Project Euclid: 25 October 2018

zbMATH: 07000592
MathSciNet: MR3874650
Digital Object Identifier: 10.1215/00127094-2018-0038

Subjects:
Primary: 22E40
Secondary: 22E41, 53C24, 57M50, 57N10, 57R20

Rights: Copyright © 2018 Duke University Press

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Vol.167 • No. 17 • 15 November 2018
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