Free products, Orbit Equivalence and Measure Equivalence Rigidity (2008)
Alvarez, Aurélien, Gaboriau, Damien
We study the analogue in orbit equivalence of free product decomposition and free indecomposability for countable groups. We introduce the (orbit equivalence invariant) notion of freely...
Free products, Orbit Equivalence and Measure Equivalence Rigidity (2008)
Alvarez, Aurélien, Gaboriau, Damien
We study the analogue in orbit equivalence of free product decomposition and free indecomposability for countable groups. We introduce the (orbit equivalence invariant) notion of freely...
Free products, Orbit Equivalence and Measure Equivalence Rigidity (2008)
Alvarez, Aurélien, Gaboriau, Damien
We study the analogue in orbit equivalence of free product decomposition and free indecomposability for countable groups. We introduce the (orbit equivalence invariant) notion of freely...
Relative Property (T) Actions and Trivial Outer Automorphism Groups (2008)
We show that every non-amenable free product of groups admits free ergodic probability measure preserving actions which have relative property (T) in the sense of S. Popa \cite[Def. 4.1]{Pop06}....
Relative Property (T) Actions and Trivial Outer Automorphism Groups (2008)
We show that every non-amenable free product of groups admits free ergodic probability measure preserving actions which have relative property (T) in the sense of S.~Popa \cite[Def. 4.1]{Pop06}....
Relative Property (T) Actions and Trivial Outer Automorphism Groups (2008)
We show that every non-amenable free product of groups admits free ergodic probability measure preserving actions which have relative property (T) in the sense of S.~Popa \cite[Def. 4.1]{Pop06}....
Free products, Orbit Equivalence and Measure Equivalence Rigidity (2008)
Alvarez, Aurélien, Gaboriau, Damien
We study the analogue in orbit equivalence of free product decomposition and free indecomposability for countable groups. We introduce the (orbit equivalence invariant) notion of freely...
Free products, Orbit Equivalence and Measure Equivalence Rigidity (2008)
Alvarez, Aurélien, Gaboriau, Damien
We study the analogue in orbit equivalence of free product decomposition and free indecomposability for countable groups. We introduce the (orbit equivalence invariant) notion of freely...
A Measurable-Group-Theoretic Solution to von Neumann's Problem (2007)
Gaboriau, Damien, Lyons, Russell
We give a positive answer, in the measurable-group-theory context, to von Neumann's problem of knowing whether a non-amenable countable discrete group contains a non-cyclic free subgroup. We also get...
A Measurable-Group-Theoretic Solution to von Neumann's Problem (2007)
Gaboriau, Damien, Lyons, Russell
We give a positive answer, in the measurable-group-theory context, to von Neumann's problem of knowing whether a non-amenable countable discrete group contains a non-cyclic free subgroup. We also get...
A Measurable-Group-Theoretic Solution to von Neumann's Problem (2007)
Gaboriau, Damien, Lyons, Russell
We give a positive answer, in the measurable-group-theory context, to von Neumann's problem of knowing whether a non-amenable countable discrete group contains a non-cyclic free subgroup. We also get...
A Measurable-Group-Theoretic Solution to von Neumann's Problem (2007)
Gaboriau, Damien, Lyons, Russell
We give a positive answer, in the measurable-group-theory context, to von Neumann's problem of knowing whether a non-amenable countable discrete group contains a non-cyclic free subgroup. We also get...
A Measurable-Group-Theoretic Solution to von Neumann's Problem (2007)
Gaboriau, Damien, Lyons, Russell
We give a positive answer, in the measurable-group-theory context, to von Neumann's problem of knowing whether a non-amenable countable discrete group contains a non-cyclic free subgroup. We also get...
A measurable-group-theoretic solution to von Neumann’s problem (2007)
Damien Gaboriau, Russell Lyons
We give a positive answer, in the measurable-group-theory context, to von Neumann’s problem of knowing whether a non-amenable countable discrete group contains a non-cyclic free subgroup. We also...
Examples of Groups that are Measure Equivalent to the Free Group (2005)
Measure Equivalence (ME) is the measure theoretic counterpart of quasi-isometry. This field grew considerably during the last years, developing tools to distinguish between different ME classes of...
Examples of Groups that are Measure Equivalent to the Free Group (2005)
Measure Equivalence (ME) is the measure theoretic counterpart of quasi-isometry. This field grew considerably during the last years, developing tools to distinguish between different ME classes of...
Examples of Groups that are Measure Equivalent to the Free Group (2005)
Measure Equivalence (ME) is the measure theoretic counterpart of quasi-isometry. This field grew considerably during the last years, developing tools to distinguish between different ME classes of...
Examples of Groups that are Measure Equivalent to the Free Group (2005)
Measure Equivalence (ME) is the measure theoretic counterpart of quasi-isometry. This field grew considerably during the last years, developing tools to distinguish between different ME classes of...
Examples of Groups that are Measure Equivalent to the Free Group (2005)
Measure Equivalence (ME) is the measure theoretic counterpart of quasi-isometry. This field grew considerably during the last years, developing tools to distinguish between different ME classes of...
An uncountable family of non orbit equivalent actions of Fn (2005)
Recall that two ergodic probability measure preserving (p.m.p.) actions σi for i =1, 2 of two countable groups Γi on probability measure standard Borel spaces (Xi,µi) areorbit equivalent (OE) if...
Invariant Percolation and Harmonic Dirichlet Functions (2004)
The main goal of this paper is to answer question 1.10 and settle conjecture 1.11 of Benjamini-Lyons-Schramm [BLS99] relating harmonic Dirichlet functions on a graph to those of the infinite clusters...
Invariant Percolation and Harmonic Dirichlet Functions (2004)
The main goal of this paper is to answer question 1.10 and settle conjecture 1.11 of Benjamini-Lyons-Schramm [BLS99] relating harmonic Dirichlet functions on a graph to those of the infinite clusters...
Invariant Percolation and Harmonic Dirichlet Functions (2004)
The main goal of this paper is to answer question 1.10 and settle conjecture 1.11 of Benjamini-Lyons-Schramm [BLS99] relating harmonic Dirichlet functions on a graph to those of the infinite clusters...
Invariant Percolation and Harmonic Dirichlet Functions (2004)
The main goal of this paper is to answer question 1.10 and settle conjecture 1.11 of Benjamini-Lyons-Schramm [BLS99] relating harmonic Dirichlet functions on a graph to those of the infinite clusters...
Invariant Percolation and Harmonic Dirichlet Functions (2004)
The main goal of this paper is to answer question 1.10 and settle conjecture 1.11 of Benjamini-Lyons-Schramm [BLS99] relating harmonic Dirichlet functions on a graph to those of the infinite clusters...
An Uncountable Family of Non Orbit Equivalent Actions of $\Bbb F_n$ (2003)
For each $2 \leq n \leq \infty$, we construct an uncountable family of free ergodic measure preserving actions $\alpha_t$ of the free group $\Bbb F_n$ on the standard probability space $(X, \mu)$...