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A construction of local Lie groupoids using Lie algebroid sprays

Banff International Research Station for Mathematical Innovation and Discovery

We give a direct, explicit and self-contained construction of a local Lie groupoid integrating a given Lie algebroid which only depends on the choice of a connection. We also give a complete account of local Lie theory based on these explicit constructions. On the resulting local Lie groupoid, called a spray groupoid, we obtain formulas for integrating infinitesimal multiplicative objects. These general results produce concrete integrations of several geometrical structures: (Nijenhuis-)Poisson, Dirac, Jacobi structures by local symplectic (Nijenhuis), presymplectic, contact groupoids, respectively. Joint work with A. Cabrera and I. Marcut.

Mathematics; Differential geometry; Topological groups, lie groups

video/mp4

Author affiliation: U F Rio de Janeiro

2017-10-16

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/63295

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/