New York Journal of Mathematics
Volume 20 (2014) 973-987


M. Kate Kearney

The stable concordance genus

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Published: October 31, 2014
Keywords: Knot concordance, genus, torus knots
Subject: 57M25

The concordance genus of a knot is the least genus of any knot in its concordance class. Although difficult to compute, it is a useful invariant that highlights the distinction between the three-genus and four-genus. In this paper we define and discuss the stable concordance genus of a knot. The stable concordance genus describes the behavior of the concordance genus under connected sum, and can be a valuable tool in calculating the concordance genus for certain families of knots. We will present several computations of the stable concordance genus and give a realization result.

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Mathematics Department, Gonzaga University, 502 E. Boone Avenue MSC 2615, Spokane, WA 99258