Thiebout Delabie

activity

20162025

most citedCoarse fundamental groups and box spaces

10 citations · 15 across the 7 of their papers we have counts for

collaborators

10 papers

math.GR2025

Measure equivalence and sofic approximations

Thiebout Delabie, Juhani Koivisto, Romain Tessera

We introduce a technique for producing a measure coupling between two sofic groups from a family of maps between their sofic approximations. We exploit this to construct measure co…

math.GR2025

$L^{p}$ measure equivalence of nilpotent groups

Thiebout Delabie, Claudio Llosa Isenrich, Romain Tessera

We classify compactly generated locally compact groups of polynomial growth up to $L^{p}$ measure equivalence (ME) for all $p \leq 1$ . To achieve this, we combine rigidity results (pr…

math.GR2024

On the stability of hyperbolicity under quantitative measure equivalence

Thiebout Delabie, Juhani Koivisto, François Le Maître +1

A well-known result of Shalom says that lattices in SO $(n, 1)$ are $L^{p}$ measure equivalent for all $p < n - 1$ . His proof actually yields the following stronger statement: the…

math.GR2021★ 1 cited

The Haagerup property and actions on von Neumann algebras

Thiebout Delabie, Alexandre Zumbrunnen

In Chapter 2 of "Groups with the Haagerup Property", Jolissaint gives on the one hand a characterization of the Haagerup property in terms of strongly mixing actions on standard pr…

math.GR2020★ 1 cited

Quantitative measure equivalence between amenable groups

Thiebout Delabie, Juhani Koivisto, François Le Maître +1

We initiate a quantitative study of measure equivalence (and orbit equivalence) between finitely generated groups, which extends the classical setting of $L^{p}$ measure equi…

math.GR2019★ 3 cited

A new characterization of the Haagerup property

Thiebout Delabie, Paul Jolissaint, Alexandre Zumbrunnen

The aim of the article is to provide a characterization of the Haagerup property for locally compact, second countable groups in terms of actions on $σ$ -finite measure spaces. It i…

math.GR2017

The asymptotic dimension of box spaces of virtually nilpotent groups

Thiebout Delabie, Matthew Tointon

We show that every box space of a virtually nilpotent group has asymptotic dimension equal to the Hirsch length of that group.

math.GR2017★ 10 cited

Coarse fundamental groups and box spaces

Thiebout Delabie, Ana Khukhro

We use a coarse version of the fundamental group first introduced by Barcelo, Kramer, Laubenbacher and Weaver to show that box spaces of finitely presented groups detect the normal…

math.GR2016

Box spaces of the free group that neither contain expanders nor embed into a Hilbert space