On sutured Floer homology and the equivalence of Seifert surfaces

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.

32 pages, 17 figures

References in corpus (4)

• Floer homology and knot complements
• Knot Floer homology detects fibred knots
• Corrigendum to "Knot Floer homology detects fibred knots"
• The decategorification of sutured Floer homology

Cited by in corpus (7)

• The decategorification of sutured Floer homology
• The Alexander module, Seifert forms, and categorification
• Splittings of knot groups
• Invariance of Immersed Floer cohomology under Maslov flows
• Sutured Floer homology distinguishes between Seifert surfaces
• Seifert surfaces distinguished by sutured Floer homology but not its Euler characteristic
• Introduction to sutured Floer homology