Horstmeyer, L.Atay, F. M.2018-04-122018-04-1220160926-2245http://hdl.handle.net/11693/36855We characterize the exact lumpability of smooth vector fields on smooth manifolds. We derive necessary and sufficient conditions for lumpability and express them from four different perspectives, thus simplifying and generalizing various results from the literature that exist for Euclidean spaces. We introduce a partial connection on the pullback bundle that is related to the Bott connection and behaves like a Lie derivative. The lumping conditions are formulated in terms of the differential of the lumping map, its covariant derivative with respect to the connection and their respective kernels. Some examples are discussed to illustrate the theory. © 2016 Published by Elsevier B.V.EnglishAggregationBott connectionDimensional reductionLumping37C1034C4058A3053B0534A05Article10.1016/j.difgeo.2016.06.0011872-6984