Adjunction inequality for spatially refined $s$-invariants

Qiuyu Ren

Vol. 344 (2026), No. 1, 145–150

DOI: 10.2140/pjm.2026.344.145

Abstract

We note an adjunction inequality in the space $k\overline{{ℂ\mathbb{P}}^2}$ for the $s$-version of the ${\mathrm{Sq}<!--FUNCTION\; APPLICATION-->}^1$-refinement of Rasmussen’s $s$-invariant. This does not hold for general spatial refinements of $s$-invariants.

Keywords

Rasmussen $s$-invariant, adjunction inequality, spatially refinement, Khovanov homology

Mathematical Subject Classification

Primary: 57K18

Secondary: 57K10, 57K40

Milestones

Received: 8 September 2025

Revised: 3 April 2026

Accepted: 21 May 2026

Published: 10 August 2026