Continuous bounded cohomology and applications to rigidity theory

By M. Burger, Nicolas Monod, A. Iozzi. 2001

229 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b69965e0ac7bf1716c825db8114b124c698e9d00

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In Algebra and Number Theory

1. Nicolas Monod
2. D. Fisher
3. Andreas Thom
4. U. Hamenstaedt
5. P. Caprace
6. Yehuda Shalom
7. M. Burger
8. K. Fujiwara

In Mathematical Physics

1. P. Caprace
2. K. Fujiwara
3. Nicolas Monod
4. Denis V. Osin
5. A. Iozzi
6. D. Fisher
7. Yehuda Shalom
8. U. Hamenstaedt

Citations in the corpus

• Isometry groups of non‐positively curved spaces: discrete subgroups (2009, background): “For detailed background on this strengthening of ergodicity introduced in [20] and on the Poisson boundary in general, we refer the reader to [54].”
• Higher Teichmüller Spaces: from SL(2,R) to other Lie groups (2010, unknown): “This follows from the theory developed in [19, 20, 83] and of which we recall a few consequences in our case at hand.”
• Bounded differential forms, generalized Milnor–Wood inequality and an application to deformation rigidity (2007, background): “Indeed, since the L-action on (∂X , ν0) is amenable, we have that ( L∞alt ( (∂X )• + 1, ν• + 10 )) is a strong resolution of R by relatively injective L-modules [20]; moreover, it is well known that, ( •(X ), d•) is a resolution of R by injective continuous L-modules, where in this case injectivity ”
• Bounded cohomology of subgroups of mapping class groups (Hyperbolic Spaces and Discrete Groups) (2000, background): “lso implies that S–arithmetic groups and certain groups of automorphisms of trees do not occur as subgroups of mapping class groups. These are the groups Γ for which Burger–Monod show QHg(Γ) = 0 [5], [3], [4]. Acknowledgments The authors would like to thank Yair Minsky and Gopal Prasad for useful di”
• Bounded cohomology and isometry groups of hyperbolic spaces (2005, methodology): “ call a lattice Γ in Girreducible if the projection of Γ into each of the factors is dense. The following lemma is part vi) of Proposition 7.13 in [MS05] and follows from the work of Burger and Monod [BM02]. Lemma 5.2: Let Γ be an irreducible lattice in a product G= G1 ×G2 of locally compact σ-compa”
• The median class and superrigidity of actions on CAT(0) cube complexes (2012, background): “According to [9], the class of c(n,R) ◦ φ(3) is the isometric image of the median class m(n,R) under the isomorphism (3.”
• A topological Tits alternative (2004, background): “of a totally disconnected group Gd with a connected center-free semisimple Lie group without compact factors Gc (see [6] Theorem 3.”
• Groups acting on manifolds: around the Zimmer program (2008, background): “This approach is similar to the proof that lattices have no C(1) actions on S(1) via bounded cohomology [21, 22, 98].”
• Isometric Embeddings in Bounded Cohomology (2013, background): “The isometric embedding Θ is in general far from being an isomorphism: for example, the real vector spaces H(2)b(Z ∗ Z) and H(3)b(Z ∗ Z) are infinite-dimensional (the case of degree 2 is dealt with in [9,16] — see also [42] for a beautiful and slick proof, and H(3)b(Z ∗ Z) is computed in [37, 48]), ”