Continuous bounded cohomology of locally compact groups
By Nicolas Ducimetière. 2000
210 citations recorded by the source corpus.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/60c43123deff9d34c68e92f655eb4e7982326fe0
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In Geometry and Topology
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Citations in the corpus
- Bounded differential forms, generalized Milnor–Wood inequality and an application to deformation rigidity (2007, background): “For the precise definitions see [20,46], while for our purpose it will suffice to say that if (S, ν) is a regular measure G-space, then the G-module Lalt(S) of L ∞ alternating functions on S is relatively injective if and only if the G-action on S is amenable in the sense of Zimmer [53].”
- Higher Teichmüller Spaces: from SL(2,R) to other Lie groups (2010, background): “Here Hcb denotes the bounded continuous cohomology for whose definition the reader is referred to [83] or also [18, § 2.”
- Cocycle superrigidity and bounded cohomology for negatively curved spaces (2004, methodology): “For a more detailed account and proofs of the statements that we merely quote, we refer the reader to [9], [30].”
- A SURVEY OF MEASURED GROUP THEORY (2009, methodology): “(Some background on bounded cohomology can be found in [88, §3] or [85]; for more details see [17, 84]).”
- C*-simplicity and the unique trace property for discrete groups (2014, background): “[40]) that a coefficient G-module (π,E) is an isometric linear G-representation π on a dual Banach space E (specifically, the dual of a separable Banach space) such that the operators in the image of π are weak*-continuous.”
- Bounded cohomology of discrete groups (2016, background): “Secondly, Monod’s book [Mon01] and Burger-Monod’s paper [BM02] already provide an excellent introduction to continuous bounded cohomology, while to the author’s knowledge no reference is available where the fundamental properties of bounded”
- Ideal bicombings for hyperbolic groups and applications (2003, methodology): “where the right hand side denotes the space of equivariant essentially bounded measurable alternating cocycles; see [5, 24].”
- Integrable measure equivalence and rigidity of hyperbolic lattices (2010, methodology): “In the Burger-Monod approach to bounded cohomology one can realize bounded cocycles in the bounded cohomology of Γ as cocycles on the boundary B.”
- Isometric Embeddings in Bounded Cohomology (2013, background): “Our construction is inspired by [24, p. 54] and exploits the approach to bounded cohomology developed by Ivanov [25], Burger and Monod [16,38].”
- Continuous bounded cohomology and applications to rigidity theory (2001, background): “Thus (15) is established (this corrects an omission in [Mo]).”
- Bounded Kähler class rigidity of actions on hermitian symmetric spaces (2002, unknown): “Thus, in the terminology of [6] and [22], c G de(cid:12)nes a continuous bounded cohomology class (cid:20) b G 2 H 2cb ( G; R ), which corresponds to (cid:20) G under the canonical isomorphism H 2cb ( G; R ) / / H c ( G; R ) (see [6]).”
- Bounded cohomology and isometry groups of hyperbolic spaces (2005, background): “,σ×σ) is ergodic. In particular, every continuous G-equivariant cocycle BT→ ℓp(G) which does not vanish identically defines a non-vanishing class in H2 b (G,ℓ p(G)) (see the discussion in Section 7 of [M01]). Thus for every f ∈ Hˆ such that ν(f) 6= 0 the class RΘ(f) does not vanish and hence the same”
- Acylindrically hyperbolic groups (2013, methodology): “The study of 1-quasi-cocycles is partially motivated by applications D. OSIN to bounded cohomology, of group von Neumann algebras, measure equivalence and orbit equivalence of groups, and low dimensional topology (see [11, 13, 25, 38, 45] and references therein).”