On the slice‐torus invariant qM from Z2‐equivariant Seiberg–Witten Floer cohomology

Nobuo Iida; Taketo Sano; Kouki Sato; Masaki Taniguchi

doi:10.1112/blms.70410

June 1, 2026Bulletin of the London Mathematical Society

On the slice‐torus invariant qM from Z2‐equivariant Seiberg–Witten Floer cohomology

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Key Points

The aim is to demonstrate that a specific slice-torus invariant cannot be formed using known invariants in the framework of Seiberg-Witten Floer cohomology.
Theoretical exploration of slice-torus invariants and their relationships with established invariants.
Comparison of Iida–Taniguchi's invariant with Rasmussen's and other known invariants.
Iida–Taniguchi's slice-torus invariant is shown to be distinct from the linear combinations of known invariants.
The findings imply limitations in the current understanding and methods of categorizing these invariants.

Implication

Shows the slice-torus invariant cannot be expressed as a linear combination of known invariants, suggesting limits of current methods.

Abstract

We show that Iida–Taniguchi's ‐valued slice‐torus invariant cannot be realized as a linear combination of Rasmussen's ‐invariant, Ozsváth–Szabó's ‐invariant, the ‐concordance invariants (), Baldwin–Sivek's instanton ‐invariant, Daemi–Imori–Sato–Scaduto–Taniguchi's instanton ‐invariant and Sano–Sato's Rasmussen‐type invariants .

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Cite This Study

Iida et al. (2026) studied this question.

synapsesocial.com/papers/6a1fc696dee9eb8c0dce79b5 https://doi.org/10.1112/blms.70410

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On the slice‐torus invariant qM from Z2‐equivariant Seiberg–Witten Floer cohomology

Key Points

Implication

Abstract

Discussion

Cite This Study

On the slice‐torus invariant qM from Z2‐equivariant Seiberg–Witten Floer cohomology

Key Points

Implication

Abstract

Discussion

Cite This Study

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