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Transactions of the American Mathematical Society

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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$.


References [Enhancements On Off] (What's this?)

  • [1] M. Culler and P. B. Shalen, Varieties of group representations and splittings of $ 3$-manifolds, Ann. of Math. (2) 117 (1983), 109-146. MR 683804 (84k:57005)
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  • [4] J. W. Morgan, Actions de groupes finis sur $ {S^3}$: la conjecture de P. A. Smith (d'apres Thurston et Meeks-Yau), Sémin. Bourbaki 578, Lecture Notes in Math., vol. 901, Springer-Verlag, Berlin and New York, pp. 277-289. MR 647502 (83h:57055)
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DOI: https://doi.org/10.1090/S0002-9947-1984-0742416-5
Article copyright: © Copyright 1984 American Mathematical Society

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