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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
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Locally free sheaves and vector bundles over smooth connected projective curve
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Question 1: this can be checked locally, on affine opens or local rings, and then becomes an exercise: if $0 \to M' \to M \overset{\pi}{\to} M'' \to 0$ is an exact sequence of …