Asymptotic Rasmussen Invariant

Sebastian Baader

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Asymptotic Rasmussen Invariant

Sebastian Baader

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Abstract

We use simple properties of the Rasmussen invariant of knots to study its asymptotic behaviour on the orbits of a smooth volume preserving vector field on a compact domain in the 3-space. A comparison with the asymptotic signature allows us to prove that asymptotic knots are non-alternating, in general. Further we show that the Rasmussen invariant defines a quasi-morphism on the braid groups and derive estimates for the stable commutator and torsion lengths of alternating braids.

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Sebastian Baader. 2007-02-12. Asymptotic Rasmussen Invariant. https://arxiv.org/abs/math/0702335

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