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), 147
MSC:
Primary 57S17; Secondary 57Q15
MathSciNet review:
534109
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Abstract: Let f be a homeomorphism of the 3sphere onto itself, of finite period n, and preserving orientation. Suppose that the fixedpoint set F of f is a tame 1sphere. It is shown that (1) the 3sphere 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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 [B]
 , Inequivalent families of periodic homeomorphisms of , Ann. of Math. (2) 80 (1964), 7893. MR 0163308 (29:611)
 [B]
 Armand Borel, Seminar on transformation groups, Ann. of Math. Studies, No. 46, Princeton Univ. Press, Princeton, N. J., 1960. MR 0116341 (22:7129)
 [B]
 Glen E. Bredon, Orientation in generalized manifolds and applications to the theory of transformation groups, Michigan Math. J. 7 (1960), 3564. MR 0116342 (22:7130)
 [E]
 C. H. Edwards, Concentricity in 3manifolds, Trans. Amer. Math. Soc. 113 (1964), 406423. MR 0178459 (31:2716)
 [FA]
 Ralph H. Fox and Emil Artin, Some wild cells and spheres in threedimensional space, Ann. of Math. (2) 49 (1948), 979990. MR 0027512 (10:317g)
 [M]
 Edwin E. Moise, Periodic homeomorphisms of the 3sphere, Illinois J. Math. 6 (1962), 206225. MR 0150768 (27:755)
 [M]
 , Affine structures in 3manifolds. IV. Piecewise linear approximations of homeomorphisms, Ann. of Math. (2) 55 (1952), 215222. MR 0046644 (13:765c)
 [M]
 , V. The triangulation theorem and Hauptvermutung, Ann. of Math. (2) 56 (1952), 96114. MR 0048805 (14:72d)
 [M]
 , VIII. Invariance of the knottypes; local tame imbedding, Ann. of Math. (2) 59 (1954), 159170. MR 0061822 (15:889g)
 [MGT]
 , Geometric topology in dimensions 2 and 3, SpringerVerlag, New York, 1977. MR 0488059 (58:7631)
 [P]
 C. D. Papakyriakopoulos, On solid tori, Proc. London Math. Soc. (3) 7 (1957), 248260. MR 0087944 (19:441d)
 [S]
 P. A. Smith, Transformations of finite period. II, Ann. of Math. (2) 40 (1939), 690711. MR 0000177 (1:30c)
 [S]
 , Periodic transformations of 3manifolds, Illinois J. Math. 9 (1965), 343348. MR 0175126 (30:5311)
 [St]
 John Stallings, On the loop theorem, Ann. of Math. (2) 72 (1960), 1219. MR 0121796 (22:12526)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197905341092
PII:
S 00029947(1979)05341092
Keywords:
Periodic homeomorphism,
3sphere,
fixedpoint set
Article copyright:
© Copyright 1979
American Mathematical Society
