Geometri och topologi: A product structure on the Floer homology of Lagrangian cobordisms

  • Datum:
  • Plats: Ångströmlaboratoriet 64119
  • Föreläsare: Noemie Legout (Shanghai Tech)
  • Kontaktperson: Maksim Maydanskiy
  • Seminarium

Abstract:

In 2015, Chantraine, Dimitroglou-Rizell, Ghiggini and Golovko [CDRGG] have defined a Floer complex associated to a pair of Lagrangian cobordisms between Legendrian submanifolds. In this talk, I will explain how to construct a product structure on it. This product recovers the cup product on singular cohomology when we consider a Lagrangian filling of a Legendrian. Moreover, we show that this product is mapped to the product on Legendrian contact cohomology by a quasi-isomorphism from the Floer complex to the Legendrian contact cohomology complex defined in [CDRGG]. Finally, we can define higher order maps to extend the product (resp. the quasi-isomorphism) to A-infinity composition maps (resp. A-infinity functor).