Lie algebroid Fibrations

Details Lie algebroid Fibrations Lie algebroid Fibrations

2010-01-27

arxiv.org/abs/1001.4904v2

Mathematics

Differential Geometry

28 pages, 1 figure

Scientific paper

10.1016/j.aim.2010.10.006

A degree 1 non-negative graded super manifold equipped with a degree 1 vector field Q satisfying [Q, Q]=1, namely a so-called NQ-1 manifold is, in plain differential geometry language, a Lie algebroid. We introduce a notion of fibration for such super manifols, that essentially involves a complete Ehresmann connection. As it is the case for Lie algebras, such fibrations turn out not to be just locally trivial products. We also define homotopy groups and prove the expected long exact sequence associated to a fibration. In particular, Crainic and Fernandes's obstruction to the integrability of Lie algebroids is interpreted as the image of a transgression map in this long exact sequence.

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