On the values taken by slice torus invariants

Abstract

We study the space of slice-torus invariants. In particular we characterize the set of values that slice-torus invariants may take on a given knot in terms of the stable smooth slice genus. Our study reveals that the resolution of the local Thom conjecture implies the existence of slice torus invariants without having to appeal to any explicit construction from a knot homology theory.

arXiv comment8 pages

References in corpus (10)

• Floer homology and knot complements
• Knot Floer homology and the four-ball genus
• Computations of the Ozsvath-Szabo knot concordance invariant
• A slice genus lower bound from sl(n) Khovanov-Rozansky homology
• Rasmussen's spectral sequences and the sl(N)-concordance invariants
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• Optimal Cobordisms between Torus Knots
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Cited by in corpus (2)

• A family of slice-torus invariants from the divisibility of Lee classes
• Hyperbolic L-space knots not concordant to algebraic knots