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The ϒ function of L –space knots is a Legendre transform
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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- Award ID(s):
- 1150872
- PAR ID:
- 10270687
- Date Published:
- Journal Name:
- Mathematical Proceedings of the Cambridge Philosophical Society
- Volume:
- 164
- Issue:
- 3
- ISSN:
- 0305-0041
- Page Range / eLocation ID:
- 401 to 411
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/S030500411700024X
