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2010 The stable $4$–genus of knots
Charles Livingston
Algebr. Geom. Topol. 10(4): 2191-2202 (2010). DOI: 10.2140/agt.2010.10.2191

Abstract

We define the stable 4–genus of a knot KS3, gst(K), to be the limiting value of g4(nK)n, where g4 denotes the 4–genus and n goes to infinity. This induces a seminorm on the rationalized knot concordance group, CQ=CQ. Basic properties of gst are developed, as are examples focused on understanding the unit ball for gst on specified subspaces of CQ. Subspaces spanned by torus knots are used to illustrate the distinction between the smooth and topological categories. A final example is given in which Casson–Gordon invariants are used to demonstrate that gst(K) can be a noninteger.

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Charles Livingston. "The stable $4$–genus of knots." Algebr. Geom. Topol. 10 (4) 2191 - 2202, 2010. https://doi.org/10.2140/agt.2010.10.2191

Information

Received: 8 September 2010; Accepted: 12 September 2010; Published: 2010
First available in Project Euclid: 19 December 2017

zbMATH: 1213.57015
MathSciNet: MR2745668
Digital Object Identifier: 10.2140/agt.2010.10.2191

Subjects:
Primary: 57M25

Rights: Copyright © 2010 Mathematical Sciences Publishers

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Vol.10 • No. 4 • 2010
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