Tag Archives: quasimorphisms

Chiral subsurface projection, asymmetric metrics and quasimorphisms

Last week I was at Oberwolfach for a meeting on geometric group theory. My friend and collaborator Koji Fujiwara gave a very nice talk about constructing actions of groups on quasi-trees (i.e. spaces quasi-isometric to trees). The construction is inspired … Continue reading

Posted in Groups, Hyperbolic geometry, Surfaces | Tagged , , , , , , , , | 4 Comments

Causal geometry

On page 10 of Besse’s famous book on Einstein manifolds one finds the following quote: It would seem that Riemannian and Lorentzian geometry have much in common: canonical connections, geodesics, curvature tensor, etc. . . . But in fact this … Continue reading

Posted in Geometric structures, Lie groups, Symplectic geometry | Tagged , , , , , , | 2 Comments

Quasimorphisms from knot invariants

Last week, Michael Brandenbursky from the Technion gave a talk at Caltech on an interesting connection between knot theory and quasimorphisms. Michael’s paper on this subject may be obtained from the arXiv. Recall that given a group , a quasimorphism … Continue reading

Posted in 3-manifolds, Groups | Tagged , , , , , , , | 2 Comments

Faces of the scl norm ball

I am in Melbourne at the moment, in the middle of giving a lecture series, as part of the 2009 Clay-Mahler lectures (also see here). Yesterday I gave a lecture with the title “faces of the scl norm ball”, and … Continue reading

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

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

Combable functions

The purpose of this post is to discuss my recent paper with Koji Fujiwara, which will shortly appear in Ergodic Theory and Dynamical Systems, both for its own sake, and in order to motivate some open questions that I find … Continue reading

Posted in Ergodic Theory | Tagged , , , , , , | 2 Comments

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