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On the homotopy and cohomology of the classifying space of Riemannian foliations
1981
Proceedings of the American Mathematical Society
Preserved Fulltext
Let G be a closed subgroup of the general linear group. Let BT^ be the classifying space for G-foliated microbundles of rank q. (The G-foliation is not assumed to be integrable.) The homotopy fiber FI"£ of the classifying map v. BT^¡ -» BG is shown to be (q -l)-connected. For the orthogonal group, this implies FRV is (q -l)-connected. The indecomposable classes in H*(RrVq) therefore are mapped to linearly independent classes in H'(FRV); the indecomposable variable classes are mapped to
doi:10.1090/s0002-9939-1981-0597668-4
fatcat:akswqr3655hpfpfcu3f3j3x6kq