Abstract
LetF be a (smooth) Γ ∞q -stucture (often called a codimension-q Haefliger structure) on a compact manifoldX n. Cohomological invariants associated to the singularities ofF are defined whose vanishing is shown to be a necessary condition for deformingF to a codimension-q foliation onX n. An analagous approach to vector bundle maps is then utilized to prove a general theorem concerning the possibility of embedding a vector bundle in the tangent bundle ofX n, and applications to the planefield problem are given. In the final section geometric realizations of the singularity classes associated toF are constructed.
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Golbus, B.F. On the singularities of foliations and of vector bundle maps. Bol. Soc. Bras. Mat 7, 11–35 (1976). https://doi.org/10.1007/BF02584845
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DOI: https://doi.org/10.1007/BF02584845