Asymptotics of the self-dual deformation complex

Details Asymptotics of the self-dual deformation complex Asymptotics of the self-dual deformation complex

2012-01-04

arxiv.org/abs/1201.1028v1

Mathematics

Differential Geometry

44 pages

Scientific paper

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 $Y^3$. 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. Applications to gluing theorems are also discussed.

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