P. Cartier. Lie groupoids, differentiable stacks, and differential Galois theory April 25–27, 2016, Independent University of Moscow, Moscow
The notion of groupoid has been important in homotopy theory (Poincare groupoid of a space). It has been extended by Ch. Ehresmann in the theory of fiber bundles. Its importance came from the efforts to understand highly singular quotient spaces, like the space of leaves in a foliation (Haefliger, Connes). In the same way as a manifold can be described by different equivalent atlases, a stack (a new kind of spaces) is described by an equivalence class of groupoids. It is possible to do differential geometry and to define topological invariants for such generalized spaces . Finally, as was first suggested by Malgrange and Umemura, in certain Galois theories (like the Picard-Vessiot theory for differential equations), Galois groupoids are better suited than Galois groups.
Cartier Pierre
Institutions
Independent University of Moscow |
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P. Cartier. Lie groupoids, differentiable stacks, and differential Galois theory, Moscow, April 25–27, 2016 |
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April 27, 2016 (Wed) |
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Lie groupoids, differentiable stacks, and differential Galois theory. Lecture 3 P. Cartier April 27, 2016, Moscow, Independent University of Moscow
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April 26, 2016 (Tue) |
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Lie groupoids, differentiable stacks, and differential Galois theory. Lecture 2 P. Cartier April 26, 2016, Moscow, Independent University of Moscow
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April 25, 2016 (Mon) |
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Lie groupoids, differentiable stacks, and differential Galois theory. Lecture 1 P. Cartier April 25, 2016, Moscow, Independent University of Moscow
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