2003/09/14 by Debra Lewis, Lewis, Debra, Nilima Nigam +4
Mathematics · Physics and Astronomy · #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #Numerical methods for differential equations #math.DG
paper · pdf · doi:10.48550/arxiv.math/0309234
29 pages
arxiv created 2003/09/14 · openalex publication_date 2003/09/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Partial connections are (singular) differential systems generalizing classical connections on principal bundles, yielding analogous decompositions for manifolds with nonfree group actions. Connection forms are interpreted as maps determining projections of the tangent bundle onto the partial connection; this approach eliminates many of the complications arising from the presence of isotropy. A connection form taking values in the dual of the Lie algebra is smooth even at singular points of the action, while analogs of the classical algebra-valued connection form are necessarily discontinuous at such points. The curvature of a partial connection form can be defined under mild technical hypotheses; the interpretation of curvature as a measure of the lack of involutivity of the (partial) connection carries over to this general setting.