Geometry and Topology Seminar

Khovanov homology is originally defined for links in S^3, and it was extended for links in I-bundles over surface by Asaeda, Przytycki and Sikora. In this talk, we will exhibit some generalization of their construction for null homologous links in RP^3. On the other side of the story, Ozsvath and Szabo defined a spectral sequence relating the Heegaard Floer homology of the branched double cover of S^3 over L to the Khovanov homology of L. We will extend this construction for null homologous links in RP^3 as well, relating the Heegaard Floer homology of the branched double cover of RP^3 over L to our Khovanov-type homology of L.