# 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} }

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

### Properly Proximal von Neumann Algebras

- 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…

### Rigidity for von Neumann algebras of graph product groups. I. Structure of automorphisms

- 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…

### First $\ell^2$-Betti numbers and proper proximality

- Mathematics
- 2022

. 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…

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