Seiberg-witten-floer Homology of a Surface times a Circle

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 Spin� 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) DOI: https://doi.org/10.1002/mana.200310277 Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: https://doi.org/10.5167/uzh-21737 Accepted Version Originally published at: Muñoz, V; Wang, B L (2005). Seiberg-Witten-Floer homology of a surface times a circle for non-torsion spin-c structures. Mathematische Nachrichten, 278(7-8):844-863. DOI: https://doi.org/10.1002/mana.200310277 ar X iv :m at h/ 99 05 05 0v 1 [ m at h. D G ] 1 0 M ay 1 99 9 SEIBERG-WITTEN-FLOER HOMOLOGY OF A SURFACE TIMES A CIRCLE VICENTE MUÑOZ AND BAI-LING WANG April, 1999 Abstract. We determine the Seiberg-Witten-Floer homology groups of the 3manifold Σ×S1, where Σ is a surface of genus g ≥ 1, together with its ring structure. 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 [22]. We determine the Seiberg-Witten-Floer homology groups of the 3manifold Σ×S1, where Σ is a surface of genus g ≥ 1, together with its ring structure. 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 [22].