# Questions tagged [pseudogroups]

The pseudogroups tag has no usage guidance.

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### Generalization of pseudogroups

Pseudogroups are defined here: https://ncatlab.org/nlab/show/pseudogroup
One of the problems with defining manifolds in terms of pseudogroups is that it gives no notion of a morphism between ...

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### A sufficient condition for $\pi_1(\operatorname B\Gamma) = 0$

I am currently reading Ghys and Sergiescu's paper Sur un groupe remarquable de difféomorphisms du cercle (French only I'm afraid), but part of their proof of Corollary 3.4 (page 20 of the pdf) is ...

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### Are linearizations of involutive PDEs locally solvable?

A possibly soft question for you guys and gals. Say a system of analytic PDEs has been completed to involution (in the sense that it's geometric symbol has a Pommaret basis, or has vanishing Spencer/...

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### Groupoids vs Pseudogroups

(Warning: I'm not an expert in the topic) Let's work in a "geometric" category, for example the category $\mathfrak{Diff}$ of "manifolds" (without the requirements of connectedness and second ...

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### Manifolds with rectifiable curves

To begin with, observe that the notion of a rectifiable curve makes sense in, say, a smooth or a PL-manifold but not in merely a topological manifold. Indeed if $f:[0,1]\rightarrow U\subset{\Bbb R}^n$...