Cocycle superrigidity and bounded cohomology for negatively curved spaces

By Nicolas Monod, Yehuda Shalom. 2004

138 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/540e7b88deb22e63cb5c87fed2c7413c7217c954

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. Thomas Sinclair
2. P. Caprace
3. Sorin Popa
4. Michah Sageev
5. I. Chifan
6. A. Furman
7. A. Iozzi
8. K. Whyte

In Mathematical Physics

1. Thomas Sinclair
2. Sorin Popa
3. I. Chifan
4. P. Caprace
5. A. Furman
6. Adrian Ioana
7. Nicolas Monod
8. A. Iozzi

Citations in the corpus

• Ideal bicombings for hyperbolic groups and applications (2003, unknown): “One of the reasons why one has to work on the boundary at infinity is that there is no known technique to show that general cocycles defined on the group itself yield non-trivial classes in bounded cohomology when one is dealing with arbitrary coefficients.”
• Cocycle and orbit equivalence superrigidity for malleable actions of w-rigid groups (2005, methodology): “s, we adopt in this paper an approach pioneered by Zimmer in the late 70’s and which has been used, in one form or another, in many OE rigidity results obtained so far ([Z2], [Ge], [GeGo], [Fu1,2,3], [MoS1,2]). The past effectiveness of this method strongly motivated us to seek a suitable cocycle sup”
• Bounded cohomology and isometry groups of hyperbolic spaces (2005, unknown): “= {0}. If Λ is a lattice in a simple Lie group of non-compact type and higher rank then the vanishing of the second bounded cohomology group H2 b (Λ,ℓ 2(Λ)) is due to Monod and Shalom (Theorem 1.4 in [MS04]). Thus in both cases, the group Λ is not measure equivalent to Γ. (Note however that for latt”
• Quasi-Actions on Trees II: Finite Depth Bass-Serre Trees (2004, background): “For instance, cocompact lattices in SL(2,R) × SL(2,R) are all quasiisometric, however, by a theorem of Margulis the irreducible ones do not split while reducible ones split as amalgams in a myriad of ways ([Mar81], and see also [MS02]).”
• ON THE STRUCTURAL THEORY OF II1 FACTORS OF NEGATIVELY CURVED GROUPS, II. ACTIONS BY PRODUCT GROUPS (2011, background): “In their fundamental works on the rigidity of group actions [17, 18], Monod and Shalom proposed a more inclusive cohomological definition of negative curvature in group theory which is given in terms of non-vanishing of the second-degree bounded cohomology for Γ with coefficients in the left-regular”
• The median class and superrigidity of actions on CAT(0) cube complexes (2012, methodology): “The vanishing or non-vanishing of bounded cohomology is not invariant under quasi-isometries (see [16, Corollary 1.7]); on the other hand, Monod–Shalom proved that vanishing of bounded cohomology with coefficients in the regular representation is invariant under measure equivalence [41] and hence in”
• Property (T) and rigidity for actions on Banach spaces (2005, result): “a superrigidity result for irreducible lattices much in the way of [Sh]. (The general idea to use irreducibility in order to transfer results from G1 ×···×Gn to Γ was also illustrated in [BMz], [BMd],[MS]; it seems to originate from the work of Margulis and [BK]; lattices in products of completely g”
• Superrigidity for irreducible lattices and geometric splitting (2005, methodology): “ity [Z]; to the geometric superrigidity of Jost-Yau [JY1],[JY2],[J] and Mok-Siu-Yeung [MSY]. Moreover, in the CAT(−1) setting, the flexibility of bounded cohomology allows for very general conclusions [MS1],[MS2], including cocycle superrigidity in the spirit of Zimmer. By contrast, the present appro”
• Simplicity and superrigidity of twin building lattices (2006, methodology): “elevant to the situation; this is done just after the statement. Since we are dealing with hyperbolic target spaces, it is most convenient to use a superrigidity theorem due to N. Monod and Y. Shalom [MS04]. Theorem 33. Let Λ be a split or almost split adjoint Kac-Moody group over Fq which is a latt”
• C∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^*$$\end{document}-simplicity and the amenable radical (2016, unknown): “We are grateful to Pierre-Emmanuel Caprace for pointing out the reference [18] to our attention.”