Displaying similar documents to “How Charles Ehresmann's vision of geometry developed with time”

In Ehresmann's footsteps: from group geometries to groupoid geometries

Jean Pradines (2007)

Banach Center Publications

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The geometric understanding of Cartan connections led Charles Ehresmann from the Erlangen program of (abstract) transformation groups to the enlarged program of Lie groupoid actions, via the basic concept of structural groupoid acting through the fibres of a (smooth) principal fibre bundle or of its associated bundles, and the basic examples stemming from the manifold of jets (fibred by its source or target projections). We show that the remarkable relation arising between the actions...

Principal bundles, groupoids, and connections

Anders Kock (2007)

Banach Center Publications

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We clarify in which precise sense the theory of principal bundles and the theory of groupoids are equivalent; and how this equivalence of theories, in the differentiable case, reflects itself in the theory of connections. The method used is that of synthetic differential geometry.

Charles Ehresmann's concepts in differential geometry

Paulette Libermann (2007)

Banach Center Publications

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We outline some of the tools C. Ehresmann introduced in Differential Geometry (fiber bundles, connections, jets, groupoids, pseudogroups). We emphasize two aspects of C. Ehresmann's works: use of Cartan notations for the theory of connections and semi-holonomic jets.

* -actions on 3 are linearizable.

Kaliman, Shulim I., Koras, Mariusz, Makar-Limanov, Leonid, Russell, Peter (1997)

Electronic Research Announcements of the American Mathematical Society [electronic only]

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