publication . Preprint . Article . 2013

On the Concordance Genus of Topologically Slice Knots

Jennifer Hom;
Open Access English
  • Published: 27 Nov 2013
Abstract
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.
Subjects
arXiv: Mathematics::Geometric TopologyMathematics::Algebraic GeometryAstrophysics::Cosmology and Extragalactic Astrophysics
free text keywords: Mathematics - Geometric Topology, 57M25, 57N70, 57R58, General Mathematics

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