35 citations · 122 across the 11 of their papers we have counts for
4 papers · 1 filter
On the holonomy of Lie algebroids
Pooja Joshi, Joel Villatoro
We introduce a holonomy groupoid for Lie algebroids. This construction generalizes both the holonomy groupoid of a foliation and the adjoint representation of a Lie algebra. We pro…
On sheaves of Lie-Rinehart algebras
Joel Villatoro
We study sheaves of Lie-Rinehart algebras over locally ringed spaces. We introduce morphisms and comorphisms of such sheaves and prove factorization theorems for each kind of morph…
Integration of singular foliations via paths
Joel Villatoro, Alfonso Garmendia
We give a new construction of the holonomy and fundamental groupoids of a singular foliation. In contrast with the existing construction of Androulidakis and Skandalis, our method…
Stacks in Poisson Geometry
Joel Villatoro
This thesis is divided into four chapters. The first chapter discusses the relationship between stacks on a site and groupoids internal to the site. It includes a rigorous proof of…