Journal of Topology· 2026Q1
The mod 2 Seiberg–Witten invariants of spin structures and spin families
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- Q1SCImago
- 2026year
Short summary
Researchers have completely determined the mod 2 Seiberg-Witten invariants for any spin structure on any closed, oriented, smooth 4-manifold, confirming the simple-type conjecture mod 2.
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Key points
- Mod 2 Seiberg-Witten invariants are fully determined for all spin structures on closed, oriented, smooth 4-manifolds.
- The simple-type conjecture mod 2 is confirmed for spin structures.
- An enhanced invariant is defined using -symmetry and localization in equivariant cohomology.
- The enhanced invariant's non-vanishing property under connected sums is key to its computation.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract We completely determine the mod 2 Seiberg–Witten invariants for any spin structure on any closed, oriented, smooth 4‐manifold . Our computation confirms the validity of the simple‐type conjecture mod 2 for spin structures. Our proof also works for families of spin 4‐manifolds and thus computes the mod 2 Seiberg–Witten invariants for spin families. The proof of our main result uses ‐symmetry to define an enhancement of the mod 2 Seiberg–Witten invariants. We prove a connected sum formula for the enhanced invariant using localisation in equivariant cohomology. Unlike the usual Seiberg–Witten invariant, the enhanced invariant does not vanish on taking connected sums and by exploiting this property, we are able to compute the enhanced invariant.
The authors' abstract, as published at the source. Journal of Topology, 2026 · DOI ↗
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Field: Geometry and Topology
Geometry and TopologyMathematics