
Let X be a compact manifold and let k be an integer. It is shown that the set of homeomorphism conjugacy classes of germs at X of foliations of codimension k and the set of homeomorphism conjugacy classes of (holonomy) representations of ∏ 1 ( X ) {\prod _1}(X) in the group of germs at 0 of 0-fixed self-diffeomorphisms of R k {{\text {R}}^k} are homeomorphic when given appropriate topologies. Stable foliation germs and stable holonomy representations correspond under this homeomorphism. It is shown that there are no stable foliation germs at a toral leaf if the dimension of the torus is greater than one.
Foliations in differential topology; geometric theory
Foliations in differential topology; geometric theory
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