On the slice-torus invariant $q_M$ from $\mathbb{Z}_2$-equivariant Seiberg--Witten Floer cohomology

Nobuo Iida; Taketo Sano; Kouki Sato; Masaki Taniguchi

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arXiv · 2501.07788

On the slice-torus invariant $q_M$ from $\mathbb{Z}_2$-equivariant Seiberg--Witten Floer cohomology

Nobuo Iida·Taketo Sano·Kouki Sato·Masaki Taniguchi

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Abstract

We show that Iida--Taniguchi's $\mathbb{Z}$-valued slice-torus invariant $q_M$ cannot be realized as a linear combination of Rasmussen's $s$-invariant, Ozsv\'ath--Szab\'o's $\tau$-invariant, all of the $\mathfrak{sl}_N$-concordance invariants ($N \geq 2$), Baldwin--Sivek's instanton $\tau$-invariant, Daemi--Imori--Sato--Scaduto--Taniguchi's instanton $\tilde{s}$-invariant and Sano--Sato's Rasmussen type invariants $\tilde{ss}_c$.

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Nobuo Iida, Taketo Sano, Kouki Sato, Masaki Taniguchi. 2025-01-14. On the slice-torus invariant $q_M$ from $\mathbb{Z}_2$-equivariant Seiberg--Witten Floer cohomology. https://arxiv.org/abs/2501.07788

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