On quasi-morphisms from knot and braid invariants

Details On quasi-morphisms from knot and braid invariants On quasi-morphisms from knot and braid invariants

2009-07-15

arxiv.org/abs/0907.2626v3

Mathematics

Geometric Topology

Abstract and title changed. This is a revised version which is accepted for publication in JKTR

Scientific paper

We study quasi-morphisms on the groups Pn of pure braids on n strings and on the group D of compactly supported area-preserving diffeomorphisms of an open two-dimensional disc. We show that it is possible to build quasi-morphisms on Pn by using knot invariants which satisfy some special properties. In particular, we study quasi-morphisms which come from knot Floer homology and Khovanov-type homology. We then discuss possible variations of the Gambaudo-Ghys construction, using the above quasi-morphisms on Pn to build quasi-morphisms on the group D of diffeomorphisms of a 2-disc.

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