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

DOI:
https://doi.org/10.1090/S0002-9939-10-10263-9

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 detects more structure of minimal genus Seifert surfaces for . 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 -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

Email:
pdhorn@math.columbia.edu

DOI:
https://doi.org/10.1090/S0002-9939-10-10263-9

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.