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The tangent microbundle of a suitable manifold

Author: Ronald J. Stern
Journal: Proc. Amer. Math. Soc. 32 (1972), 324-326
MSC: Primary 57A55
MathSciNet review: 0292087
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Abstract: The purpose of this note is to generalize to the topological category the fact that a suitable differentiable manifold is parallelizable (Theorem 4 of [1]). This result has a ``folk-theorem'' status in some quarters, but I believe that in view of the recent interest in H-manifolds [2], it would be desirable to have the result on record.

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  • [1] R. F. Brown, On suitable manifolds, Math. Scand. 14 (1964), 174-178. MR 30 #3476. MR 0173263 (30:3476)
  • [2] Morton Curtis, Finite dimensional H-spaces, Bull. Amer. Math. Soc. 77 (1971), 1-12. MR 0278303 (43:4033)
  • [3] J. Milnor, Microbundles. I, Topology 3 (1964), suppl. 1, 53-80. MR 28 #4553b. MR 0161346 (28:4553b)
  • [4] J. H. C. Whitehead, Manifolds with transverse fields in euclidean space, Ann. of Math. (2) 73 (1961), 154-212. MR 23 #A2225. MR 0124917 (23:A2225)

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Keywords: Tangent microbundle, topological parallelizability, suitable manifolds, H-spaces
Article copyright: © Copyright 1972 American Mathematical Society

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