Morita Invariance of Intrinsic Characteristic Classes of Lie Algebroids

TL;DR

This paper proves that intrinsic characteristic classes of Lie algebroids are functorial and weak Morita invariants, extending previous results by removing connectivity assumptions and generalizing their invariance properties.

Contribution

It demonstrates that these classes behave functorially under transverse maps and are invariant under Morita equivalences without connectivity restrictions.

Findings

Intrinsic characteristic classes are functorial under transverse maps.

They are weak Morita invariants of Lie algebroids.

The connectivity assumption in previous invariance results is unnecessary.

Abstract

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].