The Integration Problem for Complex Lie Algebroids

Details The Integration Problem for Complex Lie Algebroids The Integration Problem for Complex Lie Algebroids

2006-01-31

arxiv.org/abs/math/0601752v1

Mathematics

Differential Geometry

21 pages

Scientific paper

A complex Lie algebroid is a complex vector bundle over a smooth (real) manifold M with a bracket on sections and an anchor to the complexified tangent bundle of M which satisfy the usual Lie algebroid axioms. A proposal is made here to integrate analytic complex Lie algebroids by using analytic continuation to a complexification of M and integration to a holomorphic groupoid. A collection of diverse examples reveal that the holomorphic stacks presented by these groupoids tend to coincide with known objects associated to structures in complex geometry. This suggests that the object integrating a complex Lie algebroid should be a holomorphic stack.

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