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The Piecewise-Linear Structure of Euclidean Space

  • John Stallings (a1)
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It is known that, for n ≤3, ‘ought to have’ can truthfully be replaced by ‘has’ (see (4), and (5), Cor. 6·6). In this paper, this conjecture will be proved for n ≥ 5. The only unsolved case then will be in dimension four.

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(1)Gugenheim, V. K. A. M., Piecewise linear isotopy and embedding of elements and spheres (I). Proc. London Math. Soc. (3), 3 (1953), 2953.
(2)van Kampen, E., On the connection between the fundamental groups of some related spaces. American J. Math. 55 (1933), 261267.
(3)McMillan, D. R. and Zeeman, E. C., On contractible open manifolds. Proc. Cambridge Philos. Soc. 58 (1962), 221224.
(4)Moise, E. E., Affine structures in 3-manifolds. V. The triangulation theorem and Hauptvermuting. Ann. of Math. (2), 56 (1952), 96114.
(5)Munkres, J., Obstructions to the smoothing of piecewise-differentiable homeomorphisms. Ann. of Math. (2), 72 (1960), 521554.
(6)Newman, M. H. A., On the superposition of n-dimensional manifolds. J. London Math. Soc. 2 (1926), 5664.
(7)Olum, P., Non-abelian cohomology and van Kampen's theorem. Ann. of Math. (2), 68 (1958), 658668.
(8)Specker, E., Die erste Cohomologiegruppe von Überlagerungen and Homotopie-Eigenschaften dreidimensionaler Mannigfaltigkeiten. Comment. Math. Helv. 23 (1949), 303333.
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(10)Whitehead, J. H. C., On C1-complexes. Ann. of Math. (2), 41 (1940), 809824.
(11)Zeeman, E. C., On polyhedral manifolds (to appear).
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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