On quasi-morphisms from knot and braid invariants

Michael Brandenbursky

doi:https://doi.org/10.1142/S0218216511009212

On quasi-morphisms from knot and braid invariants

Research output: Contribution to journal › Article › peer-review

Abstract

We study quasi-morphisms on the groups P_n of pure braids on n strings and on the group D of compactly supported area-preserving diffeomorphisms of an open two-dimensional disk. We show that it is possible to build quasi-morphisms on P_n 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 GambaudoGhys construction, using the above quasi-morphisms on P_n to build quasi-morphisms on the group D of diffeomorphisms of a 2-disk.

Original language	American English
Pages (from-to)	1397-1417
Number of pages	21
Journal	Journal of Knot Theory and its Ramifications
Volume	20
Issue number	10
DOIs	https://doi.org/10.1142/S0218216511009212
State	Published - 1 Oct 2011
Externally published	Yes

Keywords

Quasi-morphisms
area-preserving diffeomorphisms
braid groups
knot concordance invariants

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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https://doi.org/10.1142/S0218216511009212

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AB - 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 disk. 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 GambaudoGhys construction, using the above quasi-morphisms on Pn to build quasi-morphisms on the group D of diffeomorphisms of a 2-disk.

KW - Quasi-morphisms

KW - area-preserving diffeomorphisms

KW - braid groups

KW - knot concordance invariants

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JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

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ER -

On quasi-morphisms from knot and braid invariants

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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