Seifert surfaces distinguished by sutured Floer homology but not its Euler characteristic

Details Seifert surfaces distinguished by sutured Floer homology but not its Euler characteristic Seifert surfaces distinguished by sutured Floer homology but not its Euler characteristic

2012-04-11

arxiv.org/abs/1204.2452v1

Mathematics

Geometric Topology

19 pages, 7 figures

Scientific paper

In this paper we find a family of knots with trivial Alexander polynomial, and construct two non-isotopic Seifert surfaces for each member in our family. In order to distinguish the surfaces we study the sutured Floer homology invariants of the sutured manifolds obtained by cutting the knot complements along the Seifert surfaces. Our examples provide the first use of sutured Floer homology, and not merely its Euler characteristic(a classical torsion), to distinguish Seifert surfaces. Our technique uses a version of Floer homology, called Longitude Floer Homology in a way that enables us to bypass the computations related to the SFH of the complement of a Seifert surface.

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