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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
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
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 4-ball genus, braids, Cochran-Orr-Teichner, knot concordance, quasimorphisms, ribbon, signature, slice
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 Bavard duality, free groups, immersions, maximal representation, quasimorphisms, Rigidity, rotation number, scl, Surfaces, Symplectic geometry
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 Burns-Hale, distortion, Dynamics, orderable groups, quasimorphisms, Thurston stability theorem
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
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
