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Each $ {\bf R}\sp{\infty }$-manifold has a unique piecewise linear $ {\bf R}\sp{\infty }$-structure


Author: Katsuro Sakai
Journal: Proc. Amer. Math. Soc. 90 (1984), 616-618
MSC: Primary 57N20; Secondary 57Q25, 58B05
DOI: https://doi.org/10.1090/S0002-9939-1984-0733416-5
MathSciNet review: 733416
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Abstract: R. E. Heisey introduced piecewise linear $ {{\mathbf{R}}^\infty }$-structures and defined piecewise linear $ {{\mathbf{R}}^\infty }$-manifolds. In this paper we show that two piecewise linear $ {{\mathbf{R}}^\infty }$-manifolds are isomorphic if they have the same homotopy type. From the Open Embedding Theorem for (topological) $ {{\mathbf{R}}^\infty }$-manifolds and this result, we have the title.


References [Enhancements On Off] (What's this?)

  • [1] R. E. Heisey, Embedding piecewise linear $ {{\mathbf{R}}^\infty }$-manifolds into $ {{\mathbf{R}}^\infty }$, Topology Proc. 6 (1981), 317-328. MR 672463 (83k:57010)
  • [2] -, Manifolds modelled on the direct limit of lines, Pacific J. Math. 102 (1982), 47-54. MR 682043 (84d:57009)
  • [3] C. P. Rourke and B. J. Sanderson, Introduction to piecewise-linear topology, Ergebnisse Math. Grenzgeb., Bd. 69, Springer-Verlag, Berlin, 1972. MR 0350744 (50:3236)
  • [4] K. Sakai, On $ {{\mathbf{R}}^\infty }$-manifolds and $ {Q^\infty }$-manifolds, Topology Appl. (to appear).

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0733416-5
Keywords: Direct limit, $ {{\mathbf{R}}^\infty }$-manifold, p.l. $ {{\mathbf{R}}^\infty }$-structure, p.l. $ {{\mathbf{R}}^\infty }$-manifold, $ {{\mathbf{R}}^\infty }$-p.l. map, $ {{\mathbf{R}}^\infty }$-p.l. isomorphism, polyhedron
Article copyright: © Copyright 1984 American Mathematical Society

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