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arXiv · 1911.05776

On the Upsilon invariant of fibered knots and right-veering open books

Dongtai He·Diana Hubbard·Linh Truong
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Abstract

We give a sufficient condition using the Ozsv\'ath-Stipsicz-Szab\'o concordance invariant Upsilon for the monodromy of the open book decomposition of a fibered knot to be right-veering. As an application, we generalize a result of Baker on ribbon concordances between fibered knots. Following Baker, we conclude that either fibered knots $K$ in $S^{3}$ satisfying that $\Upsilon'(t) = -g(K)$ for some $t \in [0,1)$ are unique in their smooth concordance classes or there exists a counterexample to the Slice-Ribbon Conjecture.

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Dongtai He, Diana Hubbard, Linh Truong. 2019-11-13. On the Upsilon invariant of fibered knots and right-veering open books. https://arxiv.org/abs/1911.05776

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