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The Piecewise-Linear Structure of Euclidean Space

  • John Stallings (a1)

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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(4) E. E. Moise , Affine structures in 3-manifolds. V. The triangulation theorem and Hauptvermuting. Ann. of Math. (2), 56 (1952), 96114.

(5) J. Munkres , Obstructions to the smoothing of piecewise-differentiable homeomorphisms. Ann. of Math. (2), 72 (1960), 521554.

(7) P. Olum , Non-abelian cohomology and van Kampen's theorem. Ann. of Math. (2), 68 (1958), 658668.

(8) E. Specker , Die erste Cohomologiegruppe von Überlagerungen and Homotopie-Eigenschaften dreidimensionaler Mannigfaltigkeiten. Comment. Math. Helv. 23 (1949), 303333.

(10) J. H. C. Whitehead , On C1-complexes. Ann. of Math. (2), 41 (1940), 809824.

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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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