2014/03/09 by Giorgio Trentinaglia, Trentinaglia, Giorgio
Mathematics · #58C30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Primary 58H05 #Secondary 53C05
paper · pdf · doi:10.48550/arxiv.1403.2071
openalex publication_date 2014/03/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Motivated by the study of a certain family of classical geometric problems we investigate the existence of multiplicative connections on proper Lie groupoids. We show that one can always deform a given connection which is only approximately multiplicative into a genuinely multiplicative connection. The proof of this fact that we present here relies on a recursive averaging technique. As an application we point out that the study of multiplicative connections on general proper Lie groupoids reduces to the study of longitudinal representations of regular groupoids. We regard our results as a preliminary step towards the elaboration of an obstruction theory for multiplicative connections.