58 citations · 225 across the 25 of their papers we have counts for
10 papers · 1 filter
Geometric differentiation of simplicial manifolds
Alejandro Cabrera, Matias del Hoyo
We provide a complete geometric solution to the problem of differentiating simplicial manifolds, extending classical Lie theory and complementing existing homotopical and formal ap…
Quotients of multiplicative forms and Poisson reduction
Alejandro Cabrera, Cristian Ortiz
In this paper we study quotients of Lie algebroids and groupoids endowed with compatible differential forms. We identify Lie theoretic conditions under which such forms become basi…
Local formulas for multiplicative forms
Alejandro Cabrera, Ioan Marcut, Maria Amelia Salazar
We provide explicit formulas for integrating multiplicative forms on local Lie groupoids in terms of infinitesimal data. Combined with our previous work [8], which constructs the l…
On local integration of Lie brackets
Alejandro Cabrera, Ioan Marcut, Maria Amelia Salazar
We give a direct, explicit and self-contained construction of a local Lie groupoid integrating a given Lie algebroid which only depends on the choice of a spray vector field liftin…
Lie theory of vector bundles, Poisson geometry and double structures
Henrique Bursztyn, Alejandro Cabrera, Matias del Hoyo
We briefly review our results on the Lie theory underlying vector bundles over Lie groupoids and Lie algebroids, pointing out the role of Poisson geometry in extending these result…
Van Est isomorphism for homogeneous cochains
Alejandro Cabrera, Thiago Drummond
VB-groupoids define a special class of Lie groupoids which carry a compatible linear structure. In this paper, we show that their differentiable cohomology admits a refinement by c…