Higher dimensional Heegaard Floer homology and applications

Abstract: We define a higher dimensional version of Heegaard Floer homology from a supporting open book of a contact structure with Weinstein pages. It depends on the choice of the open book, but one can use a “contact class” element to study the contact structure. In specific cases, we recover a close cousin of the Khovanov homology of a link in the 3-sphere and propose an extension to braids in 3-manifolds that fiber over the circle. This is a joint work with Ko Honda and Yin Tian.