We present a refinement of the Ozsvath-Szabo contact invariant in Heegaard Floer theory. This invariant, denoted b, takes values in the positive integers union infinity, and extends the usual contact invariant in the sense that if c(Y,\xi) is nonzero, then b is infinity. We further show that if (Y,\xi) is overtwisted, then b(Y,\xi) = 1, reflecting the usual vanishing of the usual contact invariant for such contact structures. In this talk, we will focus on the construction of b and discuss some of its basic properties and applications.
A refinement of the Ozsvath-Szabo contact invariant