Asymptotics of the Self-Dual Deformation Complex

Abstract

We analyze the indicial roots of the self-dual deformation complex on a cylinder $(\mathbb{R}\times Y^{3}, dt^{2} + g_{Y})$ , where Y 3 is a space of constant curvature. An application is the optimal decay rate of solutions on a self-dual manifold with cylindrical ends having cross-section Y 3, which is crucial in gluing results for orbifolds in the case of cross-section Y 3=S 3/Γ. We also resolve a conjecture of Kovalev–Singer in the case where Y 3 is a hyperbolic rational homology 3-sphere, and show that there are infinitely many examples for which the conjecture is true, and infinitely many examples for which the conjecture is false.