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On a Theorem of Kuiper

Published online by Cambridge University Press:  20 November 2018

Robert Wells  and
Luiz A. Favaro
Robert Wells
Affiliation:
The Pennsylvania State University, University Park, Pennsylvania
Luiz A. Favaro
Affiliation:
The Pennsylvania State University, University Park, Pennsylvania
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Let be the standard (n + 1) simplex with its standard triangulation. By the Generalized Poincare Conjecture, if n ≧ 5 and is a smooth homotopy w-sphere, then there exists a smooth triangulation , where K is a suitable subdivision of . On the other hand, in [3], N. Kuiper proves the following theorem.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 1 , 01 February 1976 , pp. 24 - 41
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Cerf, J., Topologie de certaines espaces de plongements, (Gauthier-Villars, Paris, 1961).Google Scholar
2. Hirsch, M. W., On combinatorial submanifolds of differentiable manifolds, Comment. Math. Helv. 36﹛ 1962), 103–111.Google Scholar
3. Kuiper, N. H., On the sm∞things of triangulated and combinatorial manifolds, pp. 3–22, Differential and Combinatorial Topology (Princeton).Google Scholar
4. Thorn, R., Les classes caractéristiques de Pontrjagin des variétés triangules, pp. 54–67, Symposium Internacional de Topologia Algebraica (Mexico, 1966).Google Scholar