Slice genus bound in DTS2 from s–invariant

Ren, Qiuyu

doi:10.2140/agt.2024.24.4115

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ISSN (electronic): 1472-2739

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Slice genus bound in $DTS^2$ from $s$–invariant

Qiuyu Ren

Algebraic & Geometric Topology 24 (2024) 4115–4125

DOI: 10.2140/agt.2024.24.4115

Abstract

We prove a recent conjecture of Manolescu and Willis which states that the $s$ –invariant of a knot in ${ℝ ℙ}^{3}$ (as defined by them) gives a lower bound on its null-homologous slice genus in the unit disk bundle of $T S^{2}$ . We also conjecture a lower bound in the more general case where the slice surface is not necessarily null-homologous, and give its proof in some special cases.

Keywords

Khovanov homology, slice genus, $s$–invariant, $\mathbb{RP}^3$

Mathematical Subject Classification

Primary: 57K18

Secondary: 57K10, 57K40

References

Publication

Received: 3 July 2023

Revised: 9 October 2023

Accepted: 13 November 2023

Published: 9 December 2024

Authors

Qiuyu Ren
Department of Mathematics University of California, Berkeley Berkeley, CA United States

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Volume 24, issue 7 (2024)