We modify the construction of knot Floer homology to produce a one-parameter family of homologies tHFK for knots in S3. These invariants can be used to give homomorphisms from the smooth concordance group C to Z, giving bounds on the four-ball genus and the concordance genus of knots. We give some applications of these homomorphisms.
All Science Journal Classification (ASJC) codes
- Knot Floer homology
- Knot homology