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Portugaliae Mathematica

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Volume 70, Issue 2, 2013, pp. 113–144
DOI: 10.4171/PM/1928

Published online: 2013-08-02

Integration of Lie algebroid comorphisms

Alberto S. Cattaneo[1], Benoit Dherin[2] and Alan Weinstein[3]

(1) Universit├Ąt Z├╝rich, Switzerland
(2) University of California, Berkeley, USA
(3) University of California, Berkeley, United States

We show that the path construction integration of Lie algebroids by Lie groupoids is an actual equivalence from the of integrable Lie algebroids and complete Lie algebroid comorphisms to the 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.

Keywords: Lie groupoids, Lie algebroids, comorphisms, Poisson manifolds, Lie Theory

Cattaneo Alberto, Dherin Benoit, Weinstein Alan: Integration of Lie algebroid comorphisms. Port. Math. 70 (2013), 113-144. doi: 10.4171/PM/1928