The SO(3) monopole cobordism and superconformal simple type

TL;DR

This paper demonstrates that the SO(3) monopole cobordism formula implies all certain four-manifolds with specific topological properties satisfy the superconformal simple type condition, supporting a conjecture on Seiberg-Witten basic classes.

Contribution

It establishes a link between the SO(3) monopole cobordism and the superconformal simple type condition for a class of four-manifolds, confirming a conjecture on basic classes.

Findings

All smooth, closed, oriented four-manifolds with specified properties satisfy superconformal simple type.

Supports the conjecture relating the number of Seiberg-Witten basic classes to topological data.

Shows the implication of the monopole cobordism formula on manifold classification.

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 $b^+\geq 3$ 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.