## Duke Mathematical Journal

### A refinement of Rasmussen’s S-invariant

#### Abstract

In a previous work, we constructed a spectrum-level refinement of Khovanov homology. This refinement induces stable cohomology operations on Khovanov homology. In this paper we show that these cohomology operations commute with cobordism maps on Khovanov homology. As a consequence we obtain a refinement of Rasmussen’s slice genus bound $s$ for each stable cohomology operation. We show that in the case of the Steenrod square $\operatorname {Sq}^{2}$ our refinement is strictly stronger than $s$.

#### Article information

Source
Duke Math. J., Volume 163, Number 5 (2014), 923-952.

Dates
First available in Project Euclid: 26 March 2014

https://projecteuclid.org/euclid.dmj/1395856219

Digital Object Identifier
doi:10.1215/00127094-2644466

Mathematical Reviews number (MathSciNet)
MR3189434

Zentralblatt MATH identifier
1350.57010

Subjects
Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Secondary: 55P42: Stable homotopy theory, spectra

#### Citation

Lipshitz, Robert; Sarkar, Sucharit. A refinement of Rasmussen’s S -invariant. Duke Math. J. 163 (2014), no. 5, 923--952. doi:10.1215/00127094-2644466. https://projecteuclid.org/euclid.dmj/1395856219

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