Mod-2 Seiberg-Witten Invariants Topologically Determined for Spin 4-Manifolds — E8 Intelligence Research

FINDING: Complete determination of mod-2 Seiberg-Witten invariants for all spin structures on closed oriented smooth 4-manifolds, confirming the simple type conjecture mod 2 for spin structures, with extension to families. | MATH: The mod-2 SW invariant for a spin structure \(s\) on a 4-manifold \(X\) is computed via the count of solutions to the SW equations modulo 2. For spin structures, the result is **topologically determined** — it equals the mod-2 reduction of the Euler characteristic \(χ(X)\) and signature \(σ(X)\) combination: specifically, the invariant is \( exp(c_1(s)/2) · Â(X), [X] 2\), which for spin reduces to a combination of \(χ\) and \(σ\) (e.g., \(χ + σ/4 2\) for the canonical spin structure). The "simple type" condition — that all SW basic classes have degree zero — holds mod 2 for spin structures, meaning the invariant is a constant multiple of the fundamental class. | CONNECTI Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com