Tag Archives: Dynamics

Amenability of Thompson’s group F?

Geometric group theory is not a coherent and unified field of enquiry so much as a collection of overlapping methods, examples, and contexts. The most important examples of groups are those that arise in nature: free groups and fundamental groups … Continue reading

Posted in Commentary, Groups | Tagged , , , , | 12 Comments

Orderability, and groups of homeomorphisms of the disk

I have struggled for a long time (and I continue to struggle) with the following question: Question: Is the group of self-homeomorphisms of the unit disk (in the plane) that fix the boundary pointwise a left-orderable group? Recall that a … Continue reading

Posted in Dynamics, Groups | Tagged , , , , , | 4 Comments

Big mapping class groups and dynamics

Mapping class groups (also called modular groups) are of central importance in many fields of geometry. If is an oriented surface (i.e. a -manifold), the group of orientation-preserving self-homeomorphisms of is a topological group with the compact-open topology. The mapping … Continue reading

Posted in Dynamics, Groups | Tagged , , , , , , , , , , , | 1 Comment