A higher-order genus invariant and knot Floer homology

Details A higher-order genus invariant and knot Floer homology A higher-order genus invariant and knot Floer homology

2009-01-14

arxiv.org/abs/0901.2095v2

Mathematics

Geometric Topology

6 pages, 5 figures

Scientific paper

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 $L^2$-signatures bound this invariant from below.

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