12/6/2007

John Baldwin
Columbia University

Comultiplication and the Ozsvath-Szabo contact invariant

Let S be a surface with boundary and suppose that g and h are diffeomorphisms of S which restrict to the identity on the boundary. I'll describe how the Ozsvath-Szabo contact invariants associated to the open books (S,g), (S,h), and (S,hg) are natural with respect to a comultiplication on the corresponding Heegaard-Floer homology groups. In particular, it follows that if the contact invariants associated to the open books (S,g) and (S,h) are non-zero, then so is the contact invariant associated to the open book (S,hg). I plan to discuss an extension of this comultiplication to HF^+ and an obstruction to the compatibility of a contact structure with a planar open book.