Actions of finite groups on homotopy $3$-spheres
HTML articles powered by AMS MathViewer
- by M. E. Feighn PDF
- Trans. Amer. Math. Soc. 284 (1984), 141-151 Request permission
Abstract:
It is conjectured that the action of a finite group of diffeomorphisms of the $3$-sphere is equivariantly diffeomorphic to a linear action. This conjecture is verified if both of the following conditions hold: (i) Each isotropy subgroup is dihedral or cyclic. (ii) There is a point with cyclic isotropy subgroup of order not $1,2,3$ or $5$.References
- Marc Culler and Peter B. Shalen, Varieties of group representations and splittings of $3$-manifolds, Ann. of Math. (2) 117 (1983), no. 1, 109–146. MR 683804, DOI 10.2307/2006973
- Michael W. Davis and John W. Morgan, Finite group actions on homotopy $3$-spheres, The Smith conjecture (New York, 1979) Pure Appl. Math., vol. 112, Academic Press, Orlando, FL, 1984, pp. 181–225. MR 758469, DOI 10.1016/S0079-8169(08)61642-6
- William H. Meeks III and Shing-Tung Yau, Group actions on $\textbf {R}^{3}$, The Smith conjecture (New York, 1979) Pure Appl. Math., vol. 112, Academic Press, Orlando, FL, 1984, pp. 167–179. MR 758468, DOI 10.1016/S0079-8169(08)61641-4
- John W. Morgan, Actions de groupes finis sur $S^{3}$: la conjecture de P. A. Smith (d’après Thurston et Meeks-Yau), Bourbaki Seminar, Vol. 1980/81, Lecture Notes in Math., vol. 901, Springer, Berlin-New York, 1981, pp. 277–289 (French). MR 647502 W. Thurston, The geometry and topology of $3$-manifolds (preprint).
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 284 (1984), 141-151
- MSC: Primary 57S17; Secondary 57S25
- DOI: https://doi.org/10.1090/S0002-9947-1984-0742416-5
- MathSciNet review: 742416