The stable 4-genus of knots - Mathematics > Geometric TopologyReport as inadecuate




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Abstract: The stable 4-genus of a knot K in 3-space is the limiting value of g 4nK-n,where g 4 denotes the 4-genus and n goes to infinity. This induces a seminormon CQ, the concordance group tensored with the rational numbers. Basicproperties of the stable genus are developed, as are examples focused onunderstanding the unit ball under this seminorm for specified subspaces of CQ.Subspaces spanned by torus knots are used to illustrate the distinction betweenthe smooth and topological categories. A final example is given in whichCasson-Gordon invariants are used to demonstrate that the stable genus can be anoninteger, something that cannot be detected by classical invariants or thosearising from Heegaard-Floer or Khovanov homology. It is unknown if the stablegenus determines a norm on CQ and no noninteger value for the stable genus isknown.



Author: Charles Livingston

Source: https://arxiv.org/



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