Tag Archives: stable commutator length

scl, sails and surgery

I have just uploaded a paper to the arXiv, entitled “Scl, sails and surgery”. The paper discusses a connection between stable commutator length in free groups and the geometry of sails. This is an interesting example of what sometimes happens … Continue reading

Posted in Convex geometry, Groups | Tagged , , , , , , , , , | 1 Comment

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 , , , , , , , , , , , | Leave a comment

Quasimorphisms and laws

A basic reference for the background to this post is my monograph. Let be a group, and let denote the commutator subgroup. Every element of can be expressed as a product of commutators; the commutator length of an element is the … Continue reading

Posted in Groups | Tagged , , , , | 3 Comments

five week plan

As an experiment, I plan to spend the next five weeks documenting my current research on this blog. This research comprises several related projects, but most are concerned in one way or another with the general program of studying the … Continue reading

Posted in Overview | Tagged , , , , | 4 Comments