Integration of Lie Algebroid Comorphisms

Alan Weinstein; Alberto S. Cattaneo; Benoit Dherin

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arxiv 1210.4443 v2 pith:U7OIM3IV submitted 2012-10-16 math.DG math.SG

Integration of Lie Algebroid Comorphisms

Alberto S. Cattaneo , Benoit Dherin , Alan Weinstein This is my paper

classification math.DG math.SG

keywords comorphismsactualalgebroidalgebroidscategorygroupoidsintegrationpoisson

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We show that the path construction integration of Lie algebroids by Lie groupoids is an actual equivalence from the category of integrable Lie algebroids and complete Lie algebroid comorphisms to the category of source 1-connected Lie groupoids and Lie groupoid comorphisms. This allows us to construct an actual symplectization functor in Poisson geometry. We include examples to show that the integrability of comorphisms and Poisson maps may not hold in the absence of a completeness assumption.

Integration of Lie Algebroid Comorphisms

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