October 20, 2006

András Juhász (Princeton)

Title: Floer homology and surface decompositions

Abstract: We define an invariant of balanced sutured manifolds called sutured Floer homology. In this talk we give a formula that shows how this invariant changes under surface decompositions. Using our formula we can simplify the proofs of a result of Ozsvath and Szabo that link Floer homology detects the Thurston norm, and a theorem of Ni that knot Floer homology detects fibred knots. We also show that for a wide class of knots if the top term of knot Floer homology has rank < 4 then the knot complement admits a depth one taut foliation.