zbMATH — the first resource for mathematics

Seiberg-Witten and Gromov invariants. (English) Zbl 0873.57017
Andersen, Jørgen Ellegaard (ed.) et al., Geometry and physics. Proceedings of the conference at Aarhus University, Aarhus, Denmark, 1995. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 184, 591-601 (1997).
This is a review on recent developments concerning the Seiberg-Witten invariants on 4-manifolds. The main result states that the two invariants in the title of the paper are equal up to sign. A very similar announcement was given by the author in [Math. Res. Lett. 2, 221-238 (1995; Zbl 0854.57020)]. Several essential parts of the proof appeared in the author’s papers [J. Am. Math. Soc. 9, No. 3, 845-918 (1996; Zbl 0867.53025) and ‘Counting pseudo-holomorphic submanifolds in dimension 4’, J. Differ. Geom. 44, 818-893 (1996)].
For the entire collection see [Zbl 0855.00020].

57N13 Topology of the Euclidean \(4\)-space, \(4\)-manifolds (MSC2010)
57R15 Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)