2011/09/21 by Madeleine Jotz, Jotz, Madeleine, Cristián Ortiz +1
Mathematics · Physics and Astronomy · #22A22 #53C12 (Primary) 53C05 (Secondary) #53D17 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1109.4515
openalex publication_date 2011/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, we study Lie groupoids equipped with multiplicative foliations and the corresponding infinitesimal data. We determine the infinitesimal counterpart of a multiplicative foliation in terms of its core and sides together with a partial connection satisfying special properties, giving rise to the concept of IM-foliation on a Lie algebroid. The main result of this paper shows that if G is a source simply connected Lie groupoid with Lie algebroid A, then there exists a one-to-one correspondence between multiplicative foliations on G and IM-foliations on the Lie algebroid A.