Computations of Heegaard Floer Homologies

Heegaard Floer homology groups were recently introduced by Ozsvath and Szabo to study properties of 3-manifolds and knots in them. The definition of the invariants rests on delicate holomorphic geometry, making the actual computations cumbersome. In the lecture we will recall the basic definitions and theorems of the theory, and show how to define the simplest version in a purely combinatorial manner. For a special class of 3-manifolds the more general version will be presented by simple combinatorial ideas through lattice homology of Nemethi.