The Integration Problem for Complex Lie Algebroids

  • Alan Weinstein
Chapter
Part of the Progress in Mathematics book series (PM, volume 252)

Abstract

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.

Key words

Lie algebroid groupoid stack involutive structure complex manifold pseudoconvex domain 
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Copyright information

© Birkhäuser Boston 2007

Authors and Affiliations

  • Alan Weinstein
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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