Publication date:
31 July 2017
Source:Advances in Mathematics, Volume 315
Author(s): Peter S. Ozsváth, András I. Stipsicz, Zoltán Szabó
We modify the construction of knot Floer homology to produce a one-parameter family of homologies tHFK for knots in $S^3$. These invariants can be used to give homomorphisms from the smooth concordance group $\mathcal{C}$ to $\mathbb{Z}$, giving bounds on the four-ball genus and the concordance genus of knots. We give some applications of these homomorphisms.