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The Piecewise-Linear Structure of Euclidean Space

Published online by Cambridge University Press:  24 October 2008

John Stallings
John Stallings
Affiliation:
Institute for Advanced Study and Princeton University
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Extract

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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 58 , Issue 3 , July 1962 , pp. 481 - 488
Copyright
Copyright © Cambridge Philosophical Society 1962

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References

REFERENCES

(1)Gugenheim, V. K. A. M., Piecewise linear isotopy and embedding of elements and spheres (I). Proc. London Math. Soc. (3), 3 (1953), 29–53.Google Scholar
(2)van Kampen, E., On the connection between the fundamental groups of some related spaces. American J. Math. 55 (1933), 261–267.Google Scholar
(3)McMillan, D. R. and Zeeman, E. C., On contractible open manifolds. Proc. Cambridge Philos. Soc. 58 (1962), 221–224.CrossRefGoogle Scholar
(4)Moise, E. E., Affine structures in 3-manifolds. V. The triangulation theorem and Hauptvermuting. Ann. of Math. (2), 56 (1952), 96–114.CrossRefGoogle Scholar
(5)Munkres, J., Obstructions to the smoothing of piecewise-differentiable homeomorphisms. Ann. of Math. (2), 72 (1960), 521–554.Google Scholar
(6)Newman, M. H. A., On the superposition of n-dimensional manifolds. J. London Math. Soc. 2 (1926), 56–64.Google Scholar
(7)Olum, P., Non-abelian cohomology and van Kampen's theorem. Ann. of Math. (2), 68 (1958), 658–668.Google Scholar
(8)Specker, E., Die erste Cohomologiegruppe von Überlagerungen and Homotopie-Eigenschaften dreidimensionaler Mannigfaltigkeiten. Comment. Math. Helv. 23 (1949), 303–333.Google Scholar
(9)Whitehead, J. H. C., Simplicial spaces, nuclei and m-groups. Proc. London Math. Soc. 45 (1939), 243–327.Google Scholar
(10)Whitehead, J. H. C., On C1-complexes. Ann. of Math. (2), 41 (1940), 809–824.Google Scholar
(11)Zeeman, E. C., On polyhedral manifolds (to appear).Google Scholar