Actions of finite groups on homotopy $3$-spheres
Author:
M. E. Feighn
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
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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 $5$.
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- 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 https://doi.org/10.1016/S0079-8169%2808%2961642-6
- William H. Meeks III and Shing-Tung Yau, Group actions on ${\bf R}^{3}$, The Smith conjecture (New York, 1979) Pure Appl. Math., vol. 112, Academic Press, Orlando, FL, 1984, pp. 167–179. MR 758468, DOI https://doi.org/10.1016/S0079-8169%2808%2961641-4
- 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).
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© Copyright 1984
American Mathematical Society