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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.

17 votes
2 answers
1k views

What is the motivation behind the characteristic variety of a D-module and what does it's ge...

Given a smooth algebraic variety $X$, and an $\mathcal{M}\in \text{Mod}(D_X)$, there is the characteristic variety of $\mathcal{M}$ defined as $$ \text{Char}(\mathcal{M}):= V\left(\sqrt{Ann(\mathcal{M …
8 votes
1 answer
676 views

Does an oriented $S^3$ fiber bundle admit the structure of a principal $SU(2)$-bundle?

Let $S \to X$ be an $S^3$-fiber bundle over a smooth manifold $X$. If $S$ is an oriented manifold does this fiber bundle admit the structure of an $SU(2)$-principal bundle? There is a similar theorem …