Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 14 (2018), 124, 12 pages      arXiv:1805.00542

Morita Invariance of Intrinsic Characteristic Classes of Lie Algebroids

Pedro Frejlich
UFRGS, Departamento de Matemática Pura e Aplicada, Porto Alegre, Brasil

Received June 18, 2018, in final form November 08, 2018; Published online November 15, 2018

In this note, we prove that intrinsic characteristic classes of Lie algebroids - which in degree one recover the modular class - behave functorially with respect to arbitrary transverse maps, and in particular are weak Morita invariants. In the modular case, this result appeared in [Kosmann-Schwarzbach Y., Laurent-Gengoux C., Weinstein A., Transform. Groups 13 (2008), 727-755], and with a connectivity assumption which we here show to be unnecessary, it appeared in [Crainic M., Comment. Math. Helv. 78 (2003), 681-721] and [Ginzburg V.L., J. Symplectic Geom. 1 (2001), 121-169].

Key words: Lie algebroids; modular class; characteristic classes; Morita equivalence.

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