The SO(3) monopole cobordism and superconformal simple type

Abstract

We show that the SO(3) monopole cobordism formula from Feehan and Leness (2002) implies that all smooth, closed, oriented four-manifolds with $b^1=0$ and $b^{+}\ge 3$ and odd with Seiberg-Witten simple type satisfy the superconformal simple type condition defined by Marino, Moore, and Peradze (1999) This implies the lower bound, conjectured by Fintushel and Stern (2001) on the number of Seiberg-Witten basic classes in terms of topological data.

32 pages, incorporating final galley proof corrections. To appear in Advances in Mathematics

References in corpus (3)

• Smooth Kuranishi atlases with isotropy
• Superconformal simple type and Witten's conjecture
• The topology of Kuranishi atlases

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• Virtual Morse-Bott index, moduli spaces of pairs, and applications to topology of smooth four-manifolds
• Gluing in geometric analysis via maps of Banach manifolds with corners and applications to gauge theory
• Blowup formulas for Segre and Verlinde numbers of surfaces and higher rank Donaldson invariants