On the kernel of the zero-surgery homomorphism from knot concordance

Abstract

Kawauchi defined a group structure on the set of homology S1×S2's under an equivalence relation called H˜-cobordism. This group receives a homomorphism from the knot concordance group, given by the operation of zero-surgery. We apply knot concordance invariants derived from knot Floer homology to study the kernel of the zero-surgery homomorphism. As a consequence, we show that the kernel contains a Z∞-subgroup generated by topologically slice knots in the smooth category.