# Bordered Heegaard Floer Homology, October/November 2008

## Master Class, by Dylan Thurston (Columbia University, NY)

**Abstract:**

Heegaard Floer homology is a homological invariant of 3-manifolds and knots whose Euler characteristic is the Alexander polynomial. It detects knot genus (or more generally the Thurston norm) and fibration, and has many other uses. It is conjecturally isomorphic to Seiberg-Witten Floer homology, and as such is essentially a 4-dimensional theory. In this series we will extend Heegaard-Floer homology to bordered 3-manifolds, i.e., 3-manifolds with parametrized boundary: To a connected, parametrized surface we associate a differential graded algebra, and to a 3-manifold with boundary we associate a differential module over that algebra, well-defined up to quasi-isomorphism. We will recall the construction of Heegaard Floer homology as we go along.

This is joint work with Robert Lipshitz and Peter Ozsváth.

### Schedule

October/November 2008

The schedule for the Master Class is as follows:

Monday 6 October 2008 (at the CTQM-Geomaps Nielsen Retreat at Sandbjerg)

Wednesday 8 October

Thursday 16 October

Wednesday 22 October

Wednesday 5 November

Wednesday 12 November

Tuesday 25 November

All lectures take place in Aud. D3 (1531.215), from 16:15-17:15.

### List of Participants

### Practical Information

**Organiser:** Jørgen Ellegaard Andersen.

### Sponsors

Supplementary funding for this master class is provided by "Forskerskole
i Matematik og anvendelser" based at the Department of
Mathematics, University of
Copenhagen.