Seiberg–Witten–Floer homology of a surface times a circle for non-torsion spinC structures

Abstract

We determine the Seiberg–Witten–Floer homology groups of the 3-manifold Σ × S1, 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 Oszv´ath and Szabo.