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The ϒ function of L–space knots is a Legendre transform

Published online by Cambridge University Press:  20 March 2017

MACIEJ BORODZIK  and
MATTHEW HEDDEN
MACIEJ BORODZIK
Affiliation:
Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland. e-mail: mcboro@mimuw.edu.pl
MATTHEW HEDDEN
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, MI 48824, U.S.A. e-mail: mhedden@math.msu.edu
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Abstract

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

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 164 , Issue 3 , May 2018 , pp. 401 - 411
Copyright
Copyright © Cambridge Philosophical Society 2017 

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