It is known that knot Floer homology detects the genus and Alexander polynomial of a knot. We investigate whether knot Floer homology of K detects more structure of minimal genus Seifert surfaces for K .We define an invariant of algebraically slice, genus one knots and provide examples to show that knot Floer homology does not detect this invariant. Finally, we remark that certain metabelian L2-signatures bound this invariant from below.
ASJC Scopus subject areas
- Applied Mathematics