Geodesic
On integral rigidity in Seiberg–Witten theory
Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e184

Voir la notice de l'article provenant de la source Cambridge University Press

We introduce a framework to prove integral rigidity results for the Seiberg–Witten invariants of a closed $4$-manifold X containing a nonseparating hypersurface Y satisfying suitable (chain-level) Floer theoretic conditions. As a concrete application, we show that if X has the homology of a four-torus, and it contains a nonseparating three-torus, then the sum of all Seiberg–Witten invariants of X is determined in purely cohomological terms.Our results can be interpreted as $(3+1)$-dimensional versions of Donaldson’s TQFT approach to the formula of Meng–Taubes, and build upon a subtle interplay between irreducible solutions to the Seiberg–Witten equations on X and reducible ones on Y and its complement. Along the way, we provide a concrete description of the associated graded map (for a suitable filtration) of the map on $\overline {\mathit {HM}}_*$ induced by a negative-definite cobordism between three-manifolds, which might be of independent interest. 
Lin, Francesco; Eismeier, Mike Miller. On integral rigidity in Seiberg–Witten theory. Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e184. doi: 10.1017/fms.2025.10133
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