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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
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The gauge group versus the diffeomorphism group of a manifold
Let $M$ be an $m$ dimensional differentiable manifold. Define $\text{Gauge}(M) := \text{C}^∞(M, \text{Aut}(TM))$ to be the group of all (smooth) fiberwise linear transformations of the tangent bundle. …