Thomas Mark
University of Virginia
Perturbed Heegaard Floer invariants and applications
Abstract: We describe a version of Heegaard Floer homology with coefficients in certain Novikov rings. The construction depends on the choice of a 2-dimensional real cohomology class; when this "perturbation" is nonzero the reducible part of the Floer homology vanishes, in close analogy with Seiberg-Witten theory. We use this construction to describe a version of Ozsvath-Szabo invariants for 4-manifolds with b^+ > 0, and to define well-behaved relative invariants for 4-manifolds with boundary. We will also describe some calculations and applications of these relative invariants.