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Seiberg-Witten-Floer homology of a surface times a circle for non-torsion spin-c structures

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Vicente Muñoz, Bai-Ling Wang

Differential Geometry · Submitted 10 May 1999

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We determine the Seiberg-Witten-Floer homology groups of the three-manifold which is the product of a surface of genus $g \geq 1$ times the circle, together with its ring structure, for spin-c structures which are non-trivial on the three-manifold.

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arXiv IDmath/9905050 (version 2)
Pith IDICGLZPPU, Pith's permanent record of this paper and its review
CitationBai-Ling Wang, Vicente Mu\~noz. "Seiberg-Witten-Floer homology of a surface times a circle for non-torsion spin-c structures." arXiv:math/9905050 (1999). https://pith.science/paper/ICGLZPPU
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,442 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.49 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.14 · compares with prior results 0.57 · mentions code or data availability 0.02.

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arXiv listing abstract v2. Results and the main claim are underlined; .

We determine the Seiberg-Witten-Floer homology groups of the three-manifold which is the product of a surface of genus $g \geq 1$ times the circle, together with its ring structure, for spin-c structures which are non-trivial on the three-manifold. We give applications to computing Seiberg-Witten invariants of four-manifolds which are connected sums along surfaces and also we reprove the higher type adjunction inequalities previously obtained by Oszv\'ath and Szab\'o.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We determine the Seiberg-Witten-Floer homology groups of the three-manifold which is the product of a surface of genus $g \geq 1$ times the circle, together with its ring structure, for spin-c structures which are non-trivial on the three-manifold. contribution 0.55 0.96 0.91 asserted 1.00
s1 We give applications to computing Seiberg-Witten invariants of four-manifolds which are connected sums along surfaces and also we reprove the higher type adjunction inequalities previously obtained by Oszv\'ath and Szab\'o. contribution 0.72 0.90 0.09 asserted 1.00

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Original abstract

We determine the Seiberg-Witten-Floer homology groups of the three-manifold which is the product of a surface of genus $g \geq 1$ times the circle, together with its ring structure, for spin-c structures which are non-trivial on the three-manifold. We give applications to computing Seiberg-Witten invariants of four-manifolds which are connected sums along surfaces and also we reprove the higher type adjunction inequalities previously obtained by Oszv\'ath and Szab\'o.

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