The SO(3) monopole cobordism and superconformal simple type

摘要

We show that the SO(3) monopole cobordism formula from [15] implies that all closed, oriented, smooth four-manifolds with b(1) = 0 and b(+) >= 3 and odd with Seiberg-Witten simple type satisfy the superconformal simple type condition defined by Marino, Moore, and Peradze [28,27]. This implies the lower bound, conjectured by Fintushel and Stern [18], on the number of Seiberg-Witten basic classes in terms of topological data. (C) 2019 Elsevier Inc. All rights reserved.