Matematiska institutionen

# Geometri och topologiseminarium

• Datum: 25 oktober, kl. 14.15
• Plats: Ångströmlaboratoriet 4004
• Föreläsare: Paolo Ghiggini (Nantes), Roman Golovko (ULB)
• Kontaktperson: Maksim Maydanskiy

Två seminarier:

14.15: A dynamical regard on knot Floer homology, Paolo Ghiggini
15.45: The wrapped Fukaya category of a Weinstein manifold is generated by the cocores of the critical Weinstein handles, Roman Golovko

A dynamical regard on knot Floer homology

Abstract: Knot Floer homology is a family of abelian groups \widehat{HFK}(Y, K, i) for a null-homologous knot K in a closed, oriented 3-manifold Y which is indexed by an integer i \in [-g, g], where g denotes the minimal genus of an embedded surface bounding K. This invariant was introduced by Ozsváth, Szabó and Rasmussen using a Lagrangian Floer homology construction. I will show that, when K is a fibred knot (i.e. Y-K fibres over S1 and K is the boundary of the closure of every fibre), the group \widehat{HFK}(Y, K, -g+1) is isomorphic to a version of the fix point Floer homology of any area-preserving representative of the monodromy of the fibration on Y-K. I will also discuss some potential applications of this isomorphism. This is a work in progress in collaboration with Gilberto Spano.

The wrapped Fukaya category of a Weinstein manifold is generated by the cocores of the critical Weinstein handles

Abstract: We decompose any object in the wrapped Fukaya category of a 2n-dimensional Weinstein manifold as a twisted complex built from the cocores of the n-dimensional handles in a Weinstein handle decomposition. This is joint work with Baptiste Chantraine, Georgios Dimitroglou Rizell and Paolo Ghiggini.