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Title:
A critical elliptic theory and its applications in higher-dimensional gauge theory
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Abstract:
The celebrated result of Lockhart-Mcowen says that on a non-compact complete manifold, a first order elliptic operator (with proper asymptotic conditions) is Fredholm between weighted Sobolev spaces if and only if the weight is not an indicial root. We show that a proper weighted Sobolev-theory exists even when the weight is an indicial root, and give the index formula. We also discuss some applications to singular $G_{2}-$instantons which converges to their tangent cones in polynomial rates.
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