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

Author:
Edwin E. Moise

Journal:
Trans. Amer. Math. Soc. **252** (1979), 1-47

MSC:
Primary 57S17; Secondary 57Q15

DOI:
https://doi.org/10.1090/S0002-9947-1979-0534109-2

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 such that *F* forms a subcomplex of and *f* is simplicial relative to . Suppose also that *F* is unknotted. It then follows that (2) *f* is conjugate to a rotation.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1979-0534109-2

Keywords:
Periodic homeomorphism,
3-sphere,
fixed-point set

Article copyright:
© Copyright 1979
American Mathematical Society