Asymptotics of the Self-Dual Deformation Complex

We analyze the indicial roots of the self-dual deformation complex on a cylinder (R x Y-3,Y- 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/Gamma. 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.