Abstract
We determine the Seiberg–Witten–Floer homology groups of the 3-manifold Σ × S 1, where Σ is a surface of genus g ≥ 2, together with its ring structure, for a Spinℂ structure with non-vanishing first Chern class. We give applications to computing Seiberg–Witten invariants of 4-manifolds which are connected sums along surfaces and also we reprove the higher type adjunction inequalities obtained by Oszváth and Szabó. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)