Free 𝑍₈ actions on 𝑆³

Ritter, Gerhard X.

doi:10.1090/S0002-9947-1973-0321078-8

Free $Z_{8}$ actions on $S^{3}$
HTML articles powered by AMS MathViewer

by Gerhard X. Ritter PDF

Trans. Amer. Math. Soc. 181 (1973), 195-212 Request permission

Abstract:

This paper is devoted to the problem of classifying periodic homeomorphisms which act freely on the $3$-sphere. The main result is the classification of free period eight actions and a generalization to free actions whose squares are topologically equivalent to orthogonal transformations. The result characterizes those $3$-manifolds which have the $3$-sphere as universal covering space and the cyclic group of order eight as fundamental group.

References

R. H. Bing, An alternative proof that $3$-manifolds can be triangulated, Ann. of Math. (2) 69 (1959), 37–65. MR 100841, DOI 10.2307/1970092
Glen E. Bredon and John W. Wood, Non-orientable surfaces in orientable $3$-manifolds, Invent. Math. 7 (1969), 83–110. MR 246312, DOI 10.1007/BF01389793
David W. Henderson, Extensions of Dehn’s lemma and the loop theorem, Trans. Amer. Math. Soc. 120 (1965), 448–469. MR 187233, DOI 10.1090/S0002-9947-1965-0187233-0
David W. Henderson, Relative general position, Pacific J. Math. 18 (1966), 513–523. MR 200933, DOI 10.2140/pjm.1966.18.513
J. F. P. Hudson, Piecewise linear topology, W. A. Benjamin, Inc., New York-Amsterdam, 1969. University of Chicago Lecture Notes prepared with the assistance of J. L. Shaneson and J. Lees. MR 0248844
G. R. Livesay, Fixed point free involutions on the $3$-sphere, Ann. of Math. (2) 72 (1960), 603–611. MR 116343, DOI 10.2307/1970232

Homotopieringe und Linsenräume

11

P. M. Rice, Free actions of $Z_{4}$ on $S^{3}$, Duke Math. J. 36 (1969), 749–751. MR 248814

Lehrbuch der Topologie

Seminar on combinatorial topology