Straightening and bounded cohomology of hyperbolic groups

By Igor Mineyev. 2001

135 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5c05768eef656be3d56c500ebbc6f6b2f7e6bced

How researchers see this paper

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

In Geometry and Topology

1. Anna Wienhard
2. A. Iozzi
3. Nicolas Monod
4. M. Burger
5. Yehuda Shalom
6. D. Groves
7. J. Manning
8. Igor Mineyev

In Mathematical Physics

1. Anna Wienhard
2. Nicolas Monod
3. A. Iozzi
4. M. Burger
5. Yehuda Shalom
6. Thomas Sinclair
7. D. Groves
8. J. Manning

Citations in the corpus

• Bounded differential forms, generalized Milnor–Wood inequality and an application to deformation rigidity (2007, background): “Moreover, as a consequence of the surjectivity of the comparison map for Gromov hyperbolic groups [36,44,45] we have immediately:”
• Continuous bounded cohomology and applications to rigidity theory (2002, result): “This is in contrast with the case of Gromov-hyperbolic groups, where the comparison map in degree two (and higher) is known to be surjective [ Mi1 ,2].”
• ON THE STRUCTURAL THEORY OF II1 FACTORS OF NEGATIVELY CURVED GROUPS, II. ACTIONS BY PRODUCT GROUPS (2011, result): “By a result of Mineyev, Monod, and Shalom [15], this condition is satisfied for any hyperbolic group—the case of vanishing first 2-Betti number is due to Mineyev [14].”
• Maximal Representations of Surface Groups: Symplectic Anosov Structures (2005, background): “unctions into the one of continuous functions gives rise to a comparison map c• G : H • cb(G,R) → H• (5.1) c(G,R) which encodes subtle properties of Gof geometric and algebraic nature. See [1], [33], [55], [18], [19, § V.13], [13], and also [8], [9], [38], [60], [2], [28], [31], [27], [3], [49], [48”
• The Baum-Connes conjecture for hyperbolic groups (2001, unknown): “Proposition 1 ([16]).”
• Hyperbolic groups admit proper affine isometric actions on lp-spaces (2004, methodology): “The author wishes to thank Igor Mineyev for very helpful comments on the exposition of this note, Erik Guentner for bringing [1] to my attention, and Nigel Higson for pointing out that an unpublished result Y. Shalom implies that Sp(n, 1) admits a proper affine isometric action on some uniformly con”
• Cocycle superrigidity and bounded cohomology for negatively curved spaces (2004, methodology): “Using Mineyev’s homological bicombing [28], it is not difficult to deduce the following result for hyperbolic groups (à la Gromov).”
• Bounded cohomology characterizes hyperbolic groups (2002, background): “(a)⇒(c) was shown in [9] for the largest class M1(G).”
• Dehn filling in relatively hyperbolic groups (2006, methodology): “However, we are only going to use the bicombing from [22] on a subset of X of uniformly bounded depth, and on such a subspace the valence is uniformly bounded, and Mineyev’s techniques apply.”