Lie II theorem for Lie algebroids via higher groupoids

Details Lie II theorem for Lie algebroids via higher groupoids Lie II theorem for Lie algebroids via higher groupoids

2006-12-31

arxiv.org/abs/math/0701024v2

Mathematics

Differential Geometry

30 pages, 4 figures, many revisions

Scientific paper

Following Sullivan's spacial realization of a differential algebra, we construct a universal integrating Lie 2-groupoid for every Lie algebroid. Then We show that unlike Lie algebras which one-to-one correspond to simply connected Lie groups, Lie algebroids (integrable or not) one-to-one correspond to a sort of etale Lie 2-groupoids with 2-connected source fibres. Finally, we discuss how to lift Lie algebroid morphisms to Lie 2-groupoid morphisms (Lie II Theorem).

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