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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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Keywords: Periodic homeomorphism, 3-sphere, fixed-point set
Article copyright: © Copyright 1979 American Mathematical Society

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