Continuous bounded cohomology and applications to rigidity theory

By M. Burger, Nicolas Monod. 2002

113 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/70242db847c778840e9f2a2b95dd64412bd6c3ed

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The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Nicolas Monod
2. P. Caprace
3. A. Iozzi
4. Yehuda Shalom
5. Anna Wienhard
6. M. Burger
7. K. Fujiwara
8. A. Furman

In Mathematical Physics

1. Nicolas Monod
2. P. Caprace
3. A. Iozzi
4. Yehuda Shalom
5. M. Burger
6. K. Fujiwara
7. Anna Wienhard
8. A. Furman

Citations in the corpus

• Surface group representations with maximal Toledo invariant (2003, background): “If G is a locally compact group, Hc(G,R) denotes the continuous cohomology with R-trivial coefficients, while Hcb(G,R) is the bounded continuous cohomology; for the general theory concerning the latter and its relation to the former, we refer to [46, 15, 8, 7].”
• Rank-One Isometries of Buildings and Quasi-Morphisms of Kac–Moody Groups (2008, methodology): “On the other hand, we know by [ BuM , Th. 20 & 21] that QH(Γ) = 0. Theorem 1.8 thus implies that H = ϕ(Γ) is transitive on the pair of distinct points of its limit set Λ.”
• Geometry of the mapping class groups I: Boundary amenability (2005, result): “As in [29], we conclude from the results of Burger and Monod [7, 8 ] that there is some i ≤ n and there is an equivariant map (G × X )/Γ → L 2 (H ) for the restriction of β to G � i × (G × X )/Γ.”
• Ideal bicombings for hyperbolic groups and applications (2003, methodology): “We need the notion of (double) Xsep-ergodicity introduced by Burger-Monod in [ BM02 ].”
• Property (T) and rigidity for actions on Banach spaces (2005, result): “Compare the similar situation for the cohomological product formulas of [Sh] and [ BMd ].”
• Double ergodicity of the Poisson boundary and applications to bounded cohomology (2003, background): “For instance, the higher degree Lyndon– Hochschild–Serre exact sequence from [ BuM , Theorem 13] (also see [M, Theorem 12.0.3]) now holds without this assumption, which leads to the following product formula (of K¨ unneth type) for continuous bounded cohomology in degree 2 with separable coefficient”
• Orbit equivalence rigidity and bounded cohomology (2006, methodology): “As mentioned earlier, our new approach to orbit equivalence rigidity uses notably the new approach to bounded cohomology recently developed by Burger-Monod [ BM2 ],[M].”
• Poisson-Furstenberg Boundaries, Large-scale Geometry and Growth of Groups (2011, methodology): “For application of this criterion, as well of the generalization of this criterion for the case of amenable extension see [58, 83, 17, 7].”