Local permutation stability

Abstract: A group \(\Gamma\) is sofic if elements of \(\Gamma\) can be distinguished by almost-actions on finite sets. It is a major unsolved problem to determine whether all groups are sofic. One approach to this problem which has gained much recent attention is that of “permutation stability”, that is, showing that almost-actions of a group are controlled by its actions. We introduce a “local” generalization of permutation stability, under which actions are replaced by partial actions. We exhibit an uncountable family of groups which are locally permutation stable but not permutation stable, coming from topological dynamics. The proof is based on a criterion for local stability of amenable groups, in terms of invariant random subgroups.

algebraic topologydifferential geometrydynamical systemsgroup theorygeometric topologysymplectic geometry

Audience: researchers in the topic

Geometry and topology online

Series comments: You can also find up-to-date information on the seminar homepage - warwick.ac.uk/fac/sci/maths/research/events/seminars/areas/geomtop/

The talks start at 13:30. Talks are typically fifty minutes long, with ten minutes for questions.