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A higher-order genus invariant and knot Floer homology

Author: Peter D. Horn
Journal: Proc. Amer. Math. Soc. 138 (2010), 2209-2215
MSC (2010): Primary 57M25
Published electronically: February 9, 2010
MathSciNet review: 2596061
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Abstract: It is known that knot Floer homology detects the genus and Alexander polynomial of a knot. We investigate whether knot Floer homology of $ K$ detects more structure of minimal genus Seifert surfaces for $ K$. We define an invariant of algebraically slice, genus one knots and provide examples to show that knot Floer homology does not detect this invariant. Finally, we remark that certain metabelian $ L^2$-signatures bound this invariant from below.

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Additional Information

Peter D. Horn
Affiliation: Department of Mathematics, Rice University–MS 136, P.O. Box 1892, Houston, Texas 7725-1892
Address at time of publication: Department of Mathematics, Columbia University, 2990 Broadway, New York, New York 10025

Received by editor(s): April 23, 2009
Received by editor(s) in revised form: July 23, 2009
Published electronically: February 9, 2010
Additional Notes: The author was partially supported by National Science Foundation grant DMS-0706929, the Lodieska Stockbridge Vaughn Fellowhip at Rice University, and the NSF Mathematical Sciences Postdoctoral Research Fellowship DMS-0902786.
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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