The Upsilon function of L-space knots is a Legendre transform
Geometric Topology
2015-06-25 v2
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.
Keywords
Cite
@article{arxiv.1505.06672,
title = {The Upsilon function of L-space knots is a Legendre transform},
author = {Maciej Borodzik and Matthew Hedden},
journal= {arXiv preprint arXiv:1505.06672},
year = {2015}
}
Comments
version 2: 13 pages. Question 1.5 asked in the first version is answered negatively