Introduction to Heegaard Floer homologies

Heegaard Floer homologies is a theory of invariants of 3-manifolds and/or links in 3-manifolds, that was discovered in 2001 by Ozsvath and Szabo. This theory allows to reprove many important facts, including Donaldson diagonalizability, Milnor conjecture and attack Berge conjecture on knots, such that surgery on them give a lens space.

A major advantage of this theory is computability: these homologies are computable for any link in S^₃ and for an arbitrary 3-manifold.

I will shortly give a rigorous definition, show how to compute it and give examples of applications.

The talk will be elementary.