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A Theorem On Fixed Points Of Involutions In S3

Published online by Cambridge University Press:  20 November 2018

Deane Montgomery  and
Hans Samelson
Deane Montgomery
Affiliation:
Institute for Advanced Study
Hans Samelson
Affiliation:
Institute for Advanced Study
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1. Introduction. Let T be an orientation-preserving homeomorphism of period two of the 3-sphere S3 onto itself; further let T be different from the identity and have at least one fixed point. It has been shown by Smith (8, p. 162) that the set F of all fixed points of T is a simple closed curve. However, very little is known about the position of F in S3.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 7 , 1955 , pp. 208 - 220
Copyright
Copyright © Canadian Mathematical Society 1955

References

1. Alexander, J. W., On the subdivision of 3-space by a polyhedron, Proc. Nat. Acad. Sci., 10 (1924), 6–8.Google Scholar
2. Eilenberg, S., Sur les transformations périodiques de la surface de la sphère, Fund. Math., 22 (1934) 28–41.Google Scholar
3. Eilenberg, S. and Steenrod, N. E., Foundations of algebraic topology, (Princeton, 1952).Google Scholar
4. Montgomery, D. and Zippin, L., Examples of transformation groups, Proc. Amer. Math. Soc, to appear.Google Scholar
5. Schreier, O., Die Untergruppen der freien Gruppen, Abh. Math. Sem. Hamburg, 5 (1927), 161–183.Google Scholar
6. Schubert, H., Knoten und Vollringe, Acta Math., 90 (1953), 132–286.Google Scholar
7. Seifert, H. and Threlfall, W., Lehrbuch der Topologie, (Leipzig, 1934).Google Scholar
8. Smith, P. A., Transformations of finite period, Ann. Math., 39 (1938), 127–164.Google Scholar