• Corpus ID: 246867526

# Proper proximality for various families of groups

@inproceedings{Ding2021ProperPF,
title={Proper proximality for various families of groups},
author={Changying Ding and Srivatsav Kunnawalkam Elayavalli},
year={2021}
}
• Published 6 July 2021
• Mathematics
In this paper, the notion of proper proximality (introduced in [BIP18]) is studied and classified in various families of groups. We show that if a group acts non-elementarily by isometries on a tree such that for any two edges, the intersection of their edge stabilizers is finite, then G is properly proximal. We show that the wreath product G ≀ H is properly proximal if and only if H is non-amenable. We then completely classify proper proximality among graph products of non-trivial groups. Our…
3 Citations
• Mathematics
• 2022
. We introduce the notion of proper proximality for ﬁnite von Neumann algebras, which naturally extends the notion of proper proximality for groups. Apart from the group von Neumann algebras of
• Mathematics
• 2022
In this paper we study various rigidity aspects of the von Neumann algebra L p Γ q where Γ is a graph product group [Gr90] whose underlying graph is a certain cycle of cliques and the vertex groups
. We show that for a countable exact group, having positive ﬁrst ℓ 2 -Betti number implies proper proximality in this sense of [BIP21]. This is achieved by showing a cocycle super-rigidty result for

## References

SHOWING 1-10 OF 31 REFERENCES

• Mathematics
• 2022
. We introduce the notion of proper proximality for ﬁnite von Neumann algebras, which naturally extends the notion of proper proximality for groups. Apart from the group von Neumann algebras of
• Mathematics
• 2020
Proper proximality of a countable group is a notion that was introduced by Boutonnet, Ioana and Peterson as a tool to study rigidity properties of certain von Neumann algebras associated to groups or
• Mathematics
• 2019
We here consider inner amenability from a geometric and group theoretical perspective. We prove that for every non-elementary action of a group $G$ on a finite dimensional irreducible CAT(0) cube
• Mathematics
Annales Scientifiques de l'École Normale Supérieure
• 2021
We introduce a wide class of countable groups, called properly proximal, which contains all non-amenable bi-exact groups, all non-elementary convergence groups, and all lattices in non-compact
In the 1970's Baudisch introduced the idea of the semifree group, that is, a group in which the only relators are commutators of generators. Baudisch was mainly concerned with subgroup problems,
• Mathematics
• 2019
We introduce a new equivalence relation on groups, which we call von Neumann equivalence, that is coarser than both measure equivalence and $W^*$-equivalence. We introduce a general procedure for
• R. Tomar
• Mathematics
Proceedings - Mathematical Sciences
• 2022
We prove that the fundamental group of a finite graph of convergence groups with parabolic edge groups is a convergence group. Using this result, under some mild assumptions, we prove a combination
This paper shows that graph products of weakly amenable discrete groups are weaklyAmenable (with Cowling-Haagerup constant 1) and constructs a wall space associated to the word length structure of a graph product and gives a method for extending completely bounded functions on discrete groups to a completely bounded function on their graph product.
• A. Ioana
• Mathematics
Proceedings of the International Congress of Mathematicians (ICM 2018)
• 2019
We survey some of the progress made recently in the classification of von Neumann algebras arising from countable groups and their measure preserving actions on probability spaces. We emphasize
Given a finite simplicial graph ℊ, and an assignment of groups to the verticles of ℊ, the graph product is the free product of the vertex groups modulo relations implying that adjacent vertex groups