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Asymptotic Vassiliev invariants for vector fields

Sebastian BaaderJulien Marché — 2012

Bulletin de la Société Mathématique de France

We analyse the asymptotical growth of Vassiliev invariants on non-periodic flow lines of ergodic vector fields on domains of 3 . More precisely, we show that the asymptotics of Vassiliev invariants is completely determined by the helicity of the vector field.

Legendrian graphs and quasipositive diagrams

Sebastian BaaderMasaharu Ishikawa — 2009

Annales de la faculté des sciences de Toulouse Mathématiques

In this paper we clarify the relationship between ribbon surfaces of Legendrian graphs and quasipositive diagrams by using certain fence diagrams. As an application, we give an alternative proof of a theorem concerning a relationship between quasipositive fiber surfaces and contact structures on S 3 . We also answer a question of L. Rudolph concerning moves of quasipositive diagrams.

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