We identify the periodic cyclic homology of the algebra of complete symbols on a differential groupoid G in terms of the cohomology of S * (G), the cosphere bundle of A(G), where A(G) is the Lie algebroid of G. We also relate the Hochschild homology of this algebra with the homogeneous Poisson homology of the space A * (G) 0 ∼ = S * (G) × (0, ∞), the dual of A(G) with the zero section removed. ...

In this note we determine the obstruction to triviality of the stack of exact vertex algebroids thereby recovering the result of [GMS]. The stack EVAOX of exact vertex OX-algebroids is a torsor under the stack in Picard groupoids ECAOX of exact Courant OX -algebroids. The latter is equivalent to the stack of torsors under ΩX −→Ω . Therefore, ECAOX -torsors are classified by H (X; ΩX −→Ω ). The ...

Considering prolongation of a Lie algebroid equipped with a spray, defining some classical tensors, we show that a Lie symmetry of a spray is a curvature collineation for these tensors.

We propose a new framework for constructing geometric and physical models on spacetimes provided with Lie algebroid symmetry, i.e. manifolds provided with additional anchor and generalized Lie algebra commutator structures. The approach is related to the geometry of moving nonholonomic frames with associated nonlinear connections. A strict application of such geometric methods to spinor fields ...

We introduce singular subalgebroids of an integrable Lie algebroid, extending the notion subalgebroid by dropping constant rank requirement. lay bases a theory for subalgebroids: we construct associated holonomy groupoids, adapting procedure Androulidakis-Skandalis foliations, in way that keeps track choice groupoid integrating ambient algebroid. The groupoids are topological and suitable nonco...