Integrable measure equivalence rigidity of right-angled Artin groups via quasi-isometry
C Horbez, J Huang - arXiv preprint arXiv:2309.12147, 2023 - arxiv.org
Let $ G $ be a right-angled Artin group with $|\mathrm {Out}(G)|<+\infty $. We prove that if a
countable group $ H $ with bounded torsion is measure equivalent to $ G $, with an $ L^ 1 …
countable group $ H $ with bounded torsion is measure equivalent to $ G $, with an $ L^ 1 …
Rigidity and classification results for large-type Artin groups
We compute the automorphism group of the intersection graph of many large-type Artin
groups. This graph is an analogue of the curve graph of mapping class groups but in the …
groups. This graph is an analogue of the curve graph of mapping class groups but in the …
Approximate lattices: structure in linear groups, definition (s) and beyond
S Machado - arXiv preprint arXiv:2306.09899, 2023 - arxiv.org
Approximate lattices are aperiodic generalisations of lattices of locally compact groups first
studied in seminal work of Yves Meyer. They are uniformly discrete approximate groups (ie …
studied in seminal work of Yves Meyer. They are uniformly discrete approximate groups (ie …
Measure equivalence classification of transvection-free right-angled Artin groups
C Horbez, J Huang - Journal de l'École polytechnique …, 2022 - numdam.org
We prove that if two transvection-free right-angled Artin groups are measure equivalent, then
they have isomorphic extension graphs. As a consequence, two right-angled Artin groups …
they have isomorphic extension graphs. As a consequence, two right-angled Artin groups …
Discretisable quasi-actions I: Topological completions and hyperbolicity
A Margolis - arXiv preprint arXiv:2207.04401, 2022 - arxiv.org
We define and develop the notion of a discretisable quasi-action. It is shown that a
cobounded quasi-action on a proper non-elementary hyperbolic space $ X $ not fixing a …
cobounded quasi-action on a proper non-elementary hyperbolic space $ X $ not fixing a …
Graphically discrete groups and rigidity
A Margolis, S Shepherd, E Stark… - arXiv preprint arXiv …, 2023 - arxiv.org
We introduce the notion of graphical discreteness to group theory. A finitely generated group
is graphically discrete if whenever it acts geometrically on a locally finite graph, the …
is graphically discrete if whenever it acts geometrically on a locally finite graph, the …
Quasi-isometric rigidity of extended admissible groups
A Margolis, HT Nguyen - arXiv preprint arXiv:2401.03635, 2024 - arxiv.org
arXiv:2401.03635v1 [math.GR] 8 Jan 2024 Page 1 QUASI-ISOMETRIC RIGIDITY OF
EXTENDED ADMISSIBLE GROUPS ALEX MARGOLIS AND HOANG THANH NGUYEN …
EXTENDED ADMISSIBLE GROUPS ALEX MARGOLIS AND HOANG THANH NGUYEN …
Weak Notions of Normality and Vanishing up to Rank in L2-Cohomology
U Bader, A Furman, R Sauer - … Mathematics Research Notices, 2014 - ieeexplore.ieee.org
We study vanishing results for L 2-cohomology of countable groups under the presence of
subgroups that satisfy some weak normality condition. As a consequence, we show that the …
subgroups that satisfy some weak normality condition. As a consequence, we show that the …
Super-rigidity and non-linearity for lattices in products
U Bader, A Furman - Compositio Mathematica, 2020 - cambridge.org
Super-rigidity and non-linearity for lattices in products Page 1 Super-rigidity and non-linearity
for lattices in products Uri Bader and Alex Furman Compositio Math. 156 (2020), 158–178 …
for lattices in products Uri Bader and Alex Furman Compositio Math. 156 (2020), 158–178 …
[HTML][HTML] Model geometries dominated by locally finite graphs
A Margolis - Advances in Mathematics, 2024 - Elsevier
We study model geometries of finitely generated groups. We show that a finitely generated
group possesses a model geometry not dominated by a locally finite graph if and only if it …
group possesses a model geometry not dominated by a locally finite graph if and only if it …