Edges, orbifolds, and Seiberg–Witten theory

Abstract

Seiberg–Witten theory is used to obtain new obstructions to the existence of Einstein metrics on 4-manifolds with conical singularities along an embedded surface. In the present article, the cone angle is required to be of the form 2π/p, p a positive integer, but we conjecture that similar results will also hold in greater generality.