Bounded cohomology of subgroups of mapping class groups (双曲空間及び離散群の研究 研究集会報告集)

By 藤原 耕二. 2001

255 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/4c604e763fd4beb728295eb05db809540f9f603f

How researchers see this paper

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

1. Denis V. Osin
2. Alessandro Sisto
3. Jason A. Behrstock
4. M. Bestvina
5. Mark F. Hagen
6. K. Fujiwara
7. Franccois Dahmani
8. Vincent Guirardel

Citations in the corpus

• Behavior of geodesic-length functions on Teichmüller space (2007, background): “Farb and Masur [FM98], Bestvina and Fujiwara [ BF02 ], as well as Hamenstadt [Ham06] have important general results on the finiteness of group homomorph images into the mapping class group.”
• The asymptotic dimension of a curve graph is finite (2005, methodology): “The curve complex of S was defined by Harvey [19] and has been successfully used in the study of mapping class groups, for example in [5, 18, 22].”
• Hyperbolic extensions of free groups (2014, background): “In particular, Proposition 6 of [BF4], implies that f 1 and f 2 are independent if and only if they do not have a common power.”
• Acylindrically hyperbolic groups (2013, methodology): “Since gx , z 0 , and gz belong to the same geodesic q , we have The following definition is due to Bestvina and Fujiwara [7].”
• Hyperbolicity of the complex of free factors (2011, background): “The action of Out(F) on F satisfies Weak Proper Discontinuity (see [6])).”
• A Characterization of Higher Rank Symmetric Spaces Via Bounded Cohomology (2007, methodology): “) On the other hand, non-elementary hyperbolic groups Γ, and indeed groups that act on δ-hyperbolic spaces with a weak proper discontinuity condition (WPD) have infinite-dimensional Q̃H(Γ) [12],[13],[14],[6].”
• Constructing group actions on quasi-trees and applications to mapping class groups (2010, background): “the other. Assume in addition that there is ν>0 such that the projection of any translate γXi to any nonparallel Xj is bounded by ν(this is equivalent to the Weak Proper Discontinuity condition of [BF02]). As above, define dπ Y (X,Z) to be diam(πγ(α∪β)) for any α∈ X, β ∈ Z, γ ∈ C. All axioms hold.”
• Rank-One Isometries of Buildings and Quasi-Morphisms of Kac–Moody Groups (2008, methodology): “Burger–Monod vanishing theorem [BuM, Th. 20 & 21] and the Bestvina–Fujiwara construction, it would yield an interesting rigidity statement for higher-rank lattices, in the same vein as those established in [ BeFu1 ] and [H3].”
• Hierarchically hyperbolic spaces I: curve complexes for cubical groups (2014, background): “(3) were proved in [BF02], [MM00], and [Iva97], respectively.”
• Measure equivalence rigidity of the mapping class group (2006, methodology): “In this direction, Farb-Masur [8], Bestvina-Fujiwara [2] and Yeung [39] studied homomorphisms from a lattice in some semisimple Lie group into the mapping class group and concluded that their images are finite.”
• Acylindrical hyperbolicity of groups acting on trees (2013, unknown): “Lemma 4.7 (Bestvina–Fujiwara) Let G be a group acting on a hyperbolic space X and containing a hyperbolic WPD element.”
• Gromov-Hyperbolicity of the ray graph and quasimorphisms on a big mapping class group (2014, methodology): “On utilisera enfin cette proposition d’une part pour construire un quasi-morphisme non trivial explicite sur (cid:128) et d’autre part pour construire des éléments de qui vérifient les conditions du théorème 1 de [5].”