Seifert surfaces distinguished by sutured Floer homology but not its Euler characteristic
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© 2015 Elsevier B.V. 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.
SubjectScience & Technology
MINIMAL SPANNING SURFACES
Published Version (Please cite this version)10.1016/j.topol.2015.01.005
Publication InfoVafaee, Faramarz (2015). Seifert surfaces distinguished by sutured Floer homology but not its Euler characteristic. Topology and its Applications, 184. pp. 72-86. 10.1016/j.topol.2015.01.005. Retrieved from https://hdl.handle.net/10161/17370.
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Phillip Griffiths Assistant Research Professor
My main research interests lie in low dimensional topology and geometry. Among others, these interests include Heegaard Floer homology and its applications, Khovanov homology, contact and symplectic geometry, and handlebody theory. A central goal of low dimensional topology is to understand three and four–dimensional spaces. Achieving this understanding is often aided through the study of knots and surfaces embedded therein, and the theory of knotted curves and surfaces have