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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Statically tame periodic homeomorphisms of compact connected $ 3$-manifolds. I. Homeomorphisms conjugate to rotations of the $ 3$-sphere


Author: Edwin E. Moise
Journal: Trans. Amer. Math. Soc. 252 (1979), 1-47
MSC: Primary 57S17; Secondary 57Q15
MathSciNet review: 534109
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Abstract: Let f be a homeomorphism of the 3-sphere onto itself, of finite period n, and preserving orientation. Suppose that the fixed-point set F of f is a tame 1-sphere. It is shown that (1) the 3-sphere has a triangulation $ K({{\textbf{S}}^3})$ such that F forms a subcomplex of $ K({{\textbf{S}}^3})$ and f is simplicial relative to $ K({{\textbf{S}}^3})$. Suppose also that F is unknotted. It then follows that (2) f is conjugate to a rotation.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1979-0534109-2
PII: S 0002-9947(1979)0534109-2
Keywords: Periodic homeomorphism, 3-sphere, fixed-point set
Article copyright: © Copyright 1979 American Mathematical Society