Sard's conjecture for degenerate Engel

2018/05/09 by Andres Perico, Perico, Andres
Mathematics · #Geometry and complex manifolds #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1805.03424

Abstract

Let D be a rank 2 bracket generating distribution on a 4 manifold, D is Engel if its growth vector is maximal. When this maximality fails the distribution is degenerate. We prove Sard's conjecture for the endpoint map in the case of degenerate Engel distributions. In this case the set of singular horizontal curves starting from the same point has measure zero: a full 2 dimensional disk.

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