Séminaires : Séminaire de Topologie

Introduced by Fukaya in his work on Morse theory, A-infinity categories and Floer homology, the Fukaya category constitutes one side of the homological mirror symmetry conjecture of Kontsevich. In this talk, I will present a topological variant of Floer homology and the Fukaya category of a Riemann surface of genus greater than one. Here an admissibility condition borrowed from Heegard Floer theory will be introduced which ensures invariance under isotopy and finiteness. Moreover, I will compute the Grothendieck group of the derived Fukaya category. If time permits, I will also discuss the induced action of the Mapping class group on the Fukaya category.