The ϒ function ofL–space knots is a Legendre transform

Abstract

AbstractGiven anL–space knot we show that its ϒ function is the Legendre transform of a counting function equivalent to thed–invariants of its large surgeries. The unknotting obstruction obtained for the ϒ function is, in the case ofL–space knots, contained in thed–invariants of large surgeries. Generalisations apply for connected sums ofL–space knots, which imply that the slice obstruction provided by ϒ on the subgroup of concordance generated byL–space knots is no finer than that provided by thed–invariants.