Transverse measures, the modular class, and a cohomology pairing for Lie algebroids
| dc.creator | Evens, Sam | |
| dc.creator | Lu, Jiang-Hua | |
| dc.creator | Weinstein, Alan | |
| dc.date | 1996-10-16 | |
| dc.date.accessioned | 2026-07-07T09:12:52Z | |
| dc.date.available | 2026-07-07T09:12:52Z | |
| dc.description | We show that every Lie algebroid $A$ over a manifold $P$ has a natural representation on the line bundle $Q_A = \wedge^{top}A \otimes \wedge^{top} T^*P$. The line bundle $Q_A$ may be viewed as the Lie algebroid analog of the orientation bundle in topology, and sections of $Q_A$ may be viewed as transverse measures to $A$. As a consequence, there is a well-defined class in the first Lie algebroid cohomology $H^1(A)$ called the modular class of the Lie algebroid $A$. This is the same as the one introduced earlier by Weinstein using the Poisson structure on $A^*$. We show that there is a natural pairing between the Lie algebroid cohomology spaces of $A$ with trivial coefficients and with coefficients in $Q_A$. This generalizes the pairing used in the Poincare duality of finite-dimensional Lie algebra cohomology. The case of holomorphic Lie algebroids is also discussed, where the existence of the modular class is connected with the Chern class of the line bundle $Q_A$. | |
| dc.identifier | https://arxiv.org/abs/dg-ga/9610008 | |
| dc.identifier | http://arxiv.org/abs/dg-ga/9610008 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152170 | |
| dc.subject | Differential Geometry | |
| dc.title | Transverse measures, the modular class, and a cohomology pairing for Lie algebroids | |
| dc.type | text |