Microbundles and Differentiable Structures |
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abelian group B₁ barycentric subdivision base space c.s.s. complex class of maps classifying space completes the proof composition Corollary 5.2 countable number defined Definition diagram differentiable structure Euclidean space exist neighborhoods f₁ Fi-l fibre dimension q finite complex finite simplicial complex form an abelian functor germ Hence homomorphism homotopy class homotopy commutative homotopy type inclusion map induced bundle inverse isomorphic isomorphism-germ J. H. C. Whitehead k-simplex Let f locally finite simplicial map f normal microbundle obstruction theory open subset orthogonal group piecewise linear PL as follows PL-homeomorphism PL-manifold of dimension PL-map f Pontrjagin classes principal bundle product MX Proof of Theorem proves Lemma s-class simplex simplicial approximation smoothable subcomplex tangent bundle tangent microbundle tangent vector bundle Thom 17 topological total space trivial bundle trivial normal bundle unique universal bundle theorem Whitney sum Y₂ Θε Θη хо