On sutured Floer homology and the equivalence of Seifert surfaces

Details On sutured Floer homology and the equivalence of Seifert surfaces On sutured Floer homology and the equivalence of Seifert surfaces

2008-11-02

arxiv.org/abs/0811.0178v1

Mathematics

Geometric Topology

32 pages, 17 figures

Scientific paper

We study the sutured Floer homology invariants of the sutured manifold obtained by cutting a knot complement along a Seifert surface, R. We show that these invariants are finer than the "top term" of the knot Floer homology, which they contain. In particular, we use sutured Floer homology to distinguish two non-isotopic minimal genus Seifert surfaces for the knot 8_3. A key ingredient for this technique is finding appropriate Heegaard diagrams for the sutured manifold associated to the complement of a Seifert surface.

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