A Dual Interpretation of the Gromov–Thurston Proof of Mostow Rigidity and Volume Rigidity for Representations of Hyperbolic Lattices
By M. Bucher, M. Burger, A. Iozzi. 2012
60 citations recorded by the source corpus.
We use bounded cohomology to define a notion of volume of an \(\operatorname{SO}(n,1)\)-valued representation of a lattice \(\varGamma<\operatorname{SO}(n,1)\) and, using this tool, we give a complete proof of the volume rigidity theorem of Francaviglia and Klaff (Geom. Dedicata 117, 111–124 (2006)) in this setting. Our approach gives in particular a proof of Thurston’s version of Gromov’s proof of Mostow Rigidity (also in the non-cocompact case), which is dual to the Gromov–Thurston proof using the simplicial volume invariant.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/3559ae890b05fae57bc39375db1f7617edd12820
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In Geometry and Topology
- A. Iozzi
- Roberto Frigerio
- M. Burger
- M. Bucher
- M. B. Pozzetti
- Anna Wienhard
- Nicolas Monod
- Yehuda Shalom
In Mathematical Physics
- A. Iozzi
- M. Burger
- Roberto Frigerio
- M. Bucher
- M. B. Pozzetti
- Anna Wienhard
- Nicolas Monod
- Yehuda Shalom
Citations in the corpus
- Isometric Embeddings in Bounded Cohomology (2013, background): “[20, 21, 23, 11] for the cusped case) and for manifolds locally isometric to the product of two hyperbolic planes [10] (see also [34,12] for the non-compact case with amenable cusp groups).”