Each $\textbf {R}^{\infty }$-manifold has a unique piecewise linear $\textbf {R}^{\infty }$-structure
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- by Katsuro Sakai PDF
- Proc. Amer. Math. Soc. 90 (1984), 616-618 Request permission
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
- Richard E. Heisey, Embedding piecewise linear $\textbf {R}^{\infty }$-manifolds into $\textbf {R}^{\infty }$, Topology Proc. 6 (1981), no. 2, 317–328 (1982). MR 672463
- Richard E. Heisey, Manifolds modelled on the direct limit of lines, Pacific J. Math. 102 (1982), no. 1, 47–54. MR 682043, DOI 10.2140/pjm.1982.102.47
- C. P. Rourke and B. J. Sanderson, Introduction to piecewise-linear topology, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 69, Springer-Verlag, New York-Heidelberg, 1972. MR 0350744, DOI 10.1007/978-3-642-81735-9 K. Sakai, On ${{\mathbf {R}}^\infty }$-manifolds and ${Q^\infty }$-manifolds, Topology Appl. (to appear).
Additional Information
- © Copyright 1984 American Mathematical Society
- 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