Product formulas along \(T^3\) for Seiberg-Witten invariants
Let \(X\) be a smooth closed 4-manifold which contains a smoothly embedded 2-torus \(T^2\) with trivial self-intersection number. If \(N\) is a regular neighborhood of \(T^2\) in \(X\) and \(Y\) is the closure of the complement of \(N\) in \(X\), let \(a,b,c\) denote the elements of a basis in \(H_1(\partial Y;\mathbb{Z})\). For each indivisible class \(\gamma= pa+qb +rc\), consider an orientation reversing diffeomorphism \(f_\gamma =\partial (D^2\times T^2) \to\partial Y\) with \((f_\gamma)_* [\partial (D^2 \times pt)] =\gamma\). The authors find interesting relations between the Seiberg-Witten invariants of the manifolds obtained by Dehn-Montesinos surgery along \(T^2\), i.e. manifolds of type \(X_\gamma =Y\cup_{f_\gamma} (D^2 \times T^2)\).
scientific article; zbMATH DE number 1130628