On the singularities of foliations and of vector bundle maps |
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Authors: | Bruce F Golbus |
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Institution: | (1) Wayne State University, Detroit, Michigan |
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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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Keywords: | |
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