Monopoles over 4–manifolds containing long necks I

Abstract

We study moduli spaces of Seiberg–Witten monopoles over ${spin}^c$ Riemannian 4–manifolds with long necks and/or tubular ends. This first part discusses compactness, exponential decay, and transversality. As applications we prove two vanishing theorems for Seiberg–Witten invariants.