The Upsilon function of L-space knots is a Legendre transform

Maciej Borodzik; Matthew Hedden

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arXiv · 1505.06672

The Upsilon function of L-space knots is a Legendre transform

Maciej Borodzik·Matthew Hedden

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Abstract

Given an L-space knot we show that its Upsilon function is the Legendre transform of a counting function equivalent to the d-invariants of its large surgeries. The unknotting obstruction obtained for the Upsilon function is, in the case of L-space knots, contained in the d-invariants of large surgeries. Generalizations apply for connected sums of L-space knots, which imply that the slice obstruction provided by Upsilon on the subgroup of concordance generated by L-space knots is no finer than that provided by the d-invariants.

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Maciej Borodzik, Matthew Hedden. 2015-05-25. The Upsilon function of L-space knots is a Legendre transform. https://arxiv.org/abs/1505.06672

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