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arXiv:1203.4594 [math.GT]AbstractReferencesReviewsResources

On the concordance genus of topologically slice knots

Jennifer Hom

Published 2012-03-20, updated 2013-10-28Version 2

The concordance genus of a knot K is the minimum Seifert genus of all knots smoothly concordant to K. Concordance genus is bounded below by the 4-ball genus and above by the Seifert genus. We give a lower bound for the concordance genus of K coming from the knot Floer complex of K. As an application, we prove that there are topologically slice knots with 4-ball genus equal to one and arbitrarily large concordance genus.

Comments: 15 pages, 11 figures, 1 table; v2: Added Proposition 3.2 and several figures; minor revisions throughout. This is the version to appear in IMRN
Categories: math.GT
Subjects: 57M25, 57N70, 57R58
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