Secondary Upsilon invariants of knots

Se-Goo Kim; Charles Livingston

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arXiv · 1610.05343

Secondary Upsilon invariants of knots

Se-Goo Kim·Charles Livingston

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Abstract

The knot invariant Upsilon, defined by Ozsvath, Stipsicz, and Szabo, induces a homomorphism from the smooth knot concordance group to the group of piecewise linear functions on the interval [0,2]. Here we define a set of related secondary invariants, each of which assigns to a knot a piecewise linear function on [0,2]. These secondary invariants provide bounds on the genus and concordance genus of knots. Examples of knots for which Upsilon vanishes but which are detected by these secondary invariants are presented.

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Se-Goo Kim, Charles Livingston. 2016-10-17. Secondary Upsilon invariants of knots. https://arxiv.org/abs/1610.05343

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