48 research outputs found
Non-unitarisable representations and random forests
We establish a connection between Dixmier's unitarisability problem and the
expected degree of random forests on a group. As a consequence, a residually
finite group is non-unitarisable if its first L2-Betti number is non-zero or if
it is finitely generated with non-trivial cost. Our criterion also applies to
torsion groups constructed by D. Osin, thus providing the first examples of
non-unitarisable groups not containing a non-Abelian free subgroup
Orbit Equivalence and Measured Group Theory
We give a survey of various recent developments in orbit equivalence and
measured group theory. This subject aims at studying infinite countable groups
through their measure preserving actions.Comment: 2010 Hyderabad ICM proceeding; Dans Proceedings of the International
Congress of Mathematicians, Hyderabad, India - International Congress of
Mathematicians (ICM), Hyderabad : India (2010
Examples of Groups that are Measure Equivalent to the Free Group
Published: Ergodic Theory & Dynam. Systems, 25 (2005), no. 6, 1809-1827.International audienceMeasure 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 countable groups. On the other hand, contructions of ME equivalent groups are very rare. We present a new method, based on a notion of measurable free-factor, and we apply it to exhibit a new family of groups that are measure equivalent to the free group. We also present a quite extensive survey on results about Measure Equivalence for countable groups
Measured Group Theory
The workshop aimed to study discrete and Lie groups and their actions using measure theoretic methods and their asymptotic invariants, such as -invariants, the rank gradient, cost, torsion growth, entropy-type invariants and invariants coming from random walks and percolation theory. The participants came from a wide range of mathematics: asymptotic group theory, geometric group theory, ergodic theory, -theory, graph convergence, representation theory, probability theory, descriptive set theory and algebraic topology