Seifert surfaces distinguished by sutured Floer homology but not its Euler characteristic
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.
Additional Information© 2015 Elsevier B.V. Received 15 May 2013; Accepted 10 January 2015; Available online 3 February 2015. I would like to thank my advisor Matthew Hedden for all his invaluable support and instructive comments during the course of this work. I am also grateful to Eaman Eftekhary, Chuck Livingston, Luke Williams, and David Krcatovich for helpful discussions and insights. Finally, I would like to thank the referee for pointing out a mistake in the proof of Proposition 3.3 in an earlier draft of this paper as well as many helpful comments.
Submitted - 1204.2452v1.pdf