# Lattice envelopes

@article{Bader2014LatticeE, title={Lattice envelopes}, author={Uri Bader and Alex Furman and Roman Sauer}, journal={Duke Mathematical Journal}, year={2014} }

We announce results about the structure and arithmeticity of all possible lattice embeddings of a class of countable groups which encompasses all linear groups with simple Zariski closure, all groups with non-vanishing first l2-Betti number, word hyperbolic groups, and, more general, convergence groups.

## 8 Citations

### An adelic arithmeticity theorem for lattices in products

- MathematicsMathematische Zeitschrift
- 2019

In this paper we prove that, under mild assumptions, a lattice in a product of semi-simple Lie group and a totally disconnected locally compact group is, in a certain sense, arithmetic. We do not…

### Non-discrete simple locally compact groups

- Mathematics
- 2016

Simple Lie groups and simple algebraic groups over local fields are the most prominent members of the class S of compactly generated non-discrete simple locally compact groups. We outline a new…

### Model geometries of finitely generated groups

- Mathematics
- 2022

. We study model geometries of ﬁnitely generated groups. If a ﬁnitely generated group does not contain a non-trivial ﬁnite rank free abelian commensurated subgroup, we show any model geometry is…

### Local-to-Global-rigidity of lattices in SL n ( 𝕂 )

- Mathematics
- 2022

A vertex-transitive graph 𝒢 is called Local-to-Global rigid if there exists R > 0 such that every other graph whose balls of radius R are isometric to the balls of radius R in 𝒢 is covered by 𝒢 .…

### Measure equivalence classification of transvection-free right-angled Artin groups

- MathematicsJournal de l’École polytechnique — Mathématiques
- 2022

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 with finite outer…

### Amenable uniformly recurrent subgroups and lattice embeddings

- MathematicsErgodic Theory and Dynamical Systems
- 2021

We study lattice embeddings for the class of countable groups $\unicode[STIX]{x1D6E4}$ defined by the property that the largest amenable uniformly recurrent subgroup…

### Local-to-Global-rigidity of graphs quasi-isometric to the Bruhat-Tits building of $PSL_n(\mathbb{Q}_p)$

- Mathematics
- 2020

A vertex-transitive graph $\mathcal{G}$ is called Local-to-Global rigid if there exists $R>0$ such that every other graph whose balls of radius $R$ are isometric to the balls of radius $R$ in…

### Local-to-Global-rigidity of lattices in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>S</mml:mi><mml:msub><mml:mi>L</mml:mi> <mml:mi>n</mml:mi> </mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>𝕂</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>

- ChemistryAnnales de l'Institut Fourier
- 2022

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### An adelic arithmeticity theorem for lattices in products

- MathematicsMathematische Zeitschrift
- 2019

In this paper we prove that, under mild assumptions, a lattice in a product of semi-simple Lie group and a totally disconnected locally compact group is, in a certain sense, arithmetic. We do not…

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We show that every subgroup of the mapping class group MCG(S )o f ac ompact surface S is either virtually abelian or it has innite dimensional second bounded cohomology. As an application, we give…

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Let k be a local eld, and GLn(k) a linear group over k. We prove that either contains a relatively open solvable subgroup, or it contains a relatively dense free subgroup. This result has…

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We complete the quasi-isometric classification of irreducible lattices in semisimple Lie groups over nondiscrete locally compact fields of characteristic zero by showing that any quasi-isometry of a…

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- Mathematics
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We show that S-arithmetic lattices in semisimple Lie groups with no rank one factors are quasi-isometrically rigid.

### Measure equivalence rigidity of the mapping class group

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We show that the mapping class group of a compact orientable surface with higher complexity satisfies the following rigidity in the sense of measure equivalence: If the mapping class group is measure…

### Weak Notions of Normality and Vanishing up to Rank in L2-Cohomology

- Mathematics
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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 L 2 -Betti numbers of…

### Non-discrete simple locally compact groups

- Mathematics
- 2016

Simple Lie groups and simple algebraic groups over local fields are the most prominent members of the class S of compactly generated non-discrete simple locally compact groups. We outline a new…

### Vanishing of $\ell ^2$-Betti numbers of locally compact groups as an invariant of coarse equivalence

- Mathematics
- 2017

We provide a short proof that the vanishing of $\ell^2$-Betti numbers of unimodular locally compact second countable groups is an invariant of coarse equivalence.