A Theorem On Fixed Points Of Involutions In S3

1 January 1955

journal article
Published by Canadian Mathematical Society in Canadian Journal of Mathematics

Vol. 7, 208-220
https://doi.org/10.4153/cjm-1955-027-1

Abstract

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.

Keywords

ORIENTATION
HOMEOMORPHISM
INTRODUCTION
FIXED POINTS
SPHERE
CURVE
SMITH
INVOLUTIONS
THEOREM

This publication has 4 references indexed in Scilit:

Knoten und Vollringe
Acta Mathematica, 1953
Transformations of Finite Period
Annals of Mathematics, 1938
Sur les transformations périodiques de la surface de sphère
Fundamenta Mathematicae, 1934
On the Subdivision of 3-Space by a Polyhedron
Proceedings of the National Academy of Sciences, 1924