On sutured Floer homology and the equivalence of Seifert surfaces

TL;DR

This paper demonstrates that sutured Floer homology invariants can distinguish non-isotopic minimal genus Seifert surfaces of the same knot, providing a finer invariant than previously used methods.

Contribution

It introduces a technique using sutured Floer homology to differentiate Seifert surfaces, surpassing the discriminative power of the top term of knot Floer homology.

Findings

Sutured Floer homology invariants are finer than the top term of knot Floer homology.

Successfully distinguished two non-isotopic minimal genus Seifert surfaces for knot 8_3.

Developed methods for constructing Heegaard diagrams for sutured manifolds.

Abstract

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.