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A Haefliger Leaf closures in Riemannian foliations
T Tsuboi On the homomorphism tf flR BDiff dR
T Mizutani The GodbillonVey cocycle of Diff U
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3-manifold action analytique complexe assume branched covering champ de vecteurs characteristic classes Chern character closed orbits closure cochain cocycle codimension codimension one foliations cohomology commutativity compact leaf complete Riemannian completes the proof complex reflection construction curve defined definition denote Department of Mathematics Diff diffeomorphic differentiable dimension equivalent equivariant Euler characteristic exists fiber fibration finite foliation function fundamental group geod geodesic H X.T Hausdorff Hence holonomy homology homomorphism homotopy implies induced induit integer invariant isolee isometries isomorphism Japan knot Lemma Let f Lie algebra loop Math monodromy morphism Morse Morse index normal obtain open sets orbifold oriented peut polyedre proof of Theorem Proposition prove pseudogroup quotient resp restriction Riemannian manifold Riemannian metric rugueux satisfies Seifert singular points singularite isolee smooth strates subgroup subset Suppose surface bundles surjective T-equivariant tangent Tokyo Topology torus tout transverse foliation trivial