Duke Mathematical Journal
- Duke Math. J.
- Volume 167, Number 17 (2018), 3129-3169.
The bounded Borel class and -manifold groups
If is a lattice, we define an invariant of a representation using the Borel class . 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 of the irreducible complex -dimensional representation of 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 as a normed space.
Duke Math. J., Volume 167, Number 17 (2018), 3129-3169.
Received: 12 February 2017
Revised: 2 July 2018
First available in Project Euclid: 25 October 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 22E40: Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx]
Secondary: 22E41: Continuous cohomology [See also 57R32, 57Txx, 58H10] 57R20: Characteristic classes and numbers 53C24: Rigidity results 57N10: Topology of general 3-manifolds [See also 57Mxx] 57M50: Geometric structures on low-dimensional manifolds
Bucher, Michelle; Burger, Marc; Iozzi, Alessandra. The bounded Borel class and $3$ -manifold groups. Duke Math. J. 167 (2018), no. 17, 3129--3169. doi:10.1215/00127094-2018-0038. https://projecteuclid.org/euclid.dmj/1540454549