## Periodic homeomorphisms of $3$-manifolds fibered over $S^{1}$

HTML articles powered by AMS MathViewer

- by Jeffrey L. Tollefson
- Trans. Amer. Math. Soc.
**223**(1976), 223-234 - DOI: https://doi.org/10.1090/S0002-9947-1976-0431177-0
- PDF | Request permission

Erratum: Trans. Amer. Math. Soc.

**243**(1978), 309-310.

## Abstract:

Two problems concerning periodic homeomorphisms of 3-manifolds are considered. The first is that of obtaining systems of incompressible surfaces invariant under a given involution. The second problem is the realization by a periodic homeomorphism of an element of finite order in the mapping class group of a 3-manifold. Solutions to both problems are obtained in certain instances.## References

- R. Baer,
- Joan S. Birman and Hugh M. Hilden,
*On isotopies of homeomorphisms of Riemann surfaces*, Ann. of Math. (2)**97**(1973), 424–439. MR**325959**, DOI 10.2307/1970830 - E. M. Brown,
*Unknotting in $M^{2}\times I$*, Trans. Amer. Math. Soc.**123**(1966), 480–505. MR**198482**, DOI 10.1090/S0002-9947-1966-0198482-0 - P. E. Conner and Frank Raymond,
*Manifolds with few periodic homeomorphisms*, Proceedings of the Second Conference on Compact Transformation Groups (Univ. Massachusetts, Amherst, Mass., 1971) Lecture Notes in Math., Vol. 299, Springer, Berlin, 1972, pp. 1–75. MR**0358835** - Paik Kee Kim and Jeffrey L. Tollefson,
*PL involutions of fibered $3$-manifolds*, Trans. Amer. Math. Soc.**232**(1977), 221–237. MR**454981**, DOI 10.1090/S0002-9947-1977-0454981-2
K. W. Kwun, - Kyung Whan Kwun and Jeffrey L. Tollefson,
*$\textrm {PL}$ involutions of $S^{1}\times S^{1}\times S^{1}$*, Trans. Amer. Math. Soc.**203**(1975), 97–106. MR**370634**, DOI 10.1090/S0002-9947-1975-0370634-1 - Jakob Nielsen,
*Abbildungsklassen endlicher Ordnung*, Acta Math.**75**(1943), 23–115 (German). MR**13306**, DOI 10.1007/BF02404101
F. Raymond and L. Scott, - Jeffrey L. Tollefson,
*$3$-manifolds fibering over $S^{1}$ with nonunique connected fiber*, Proc. Amer. Math. Soc.**21**(1969), 79–80. MR**236945**, DOI 10.1090/S0002-9939-1969-0236945-8 - Jeffrey L. Tollefson,
*Homotopically trivial periodic homeomorphisms on $3$-manifolds*, Ann. of Math. (2)**97**(1973), 14–26. MR**309105**, DOI 10.2307/1970875 - Jeffrey L. Tollefson,
*Involutions on $S^{1}\times S^{2}$ and other $3$-manifolds*, Trans. Amer. Math. Soc.**183**(1973), 139–152. MR**326738**, DOI 10.1090/S0002-9947-1973-0326738-0 - Friedhelm Waldhausen,
*On irreducible $3$-manifolds which are sufficiently large*, Ann. of Math. (2)**87**(1968), 56–88. MR**224099**, DOI 10.2307/1970594 - H. Zieschang, E. Vogt, and H.-D. Coldewey,
*Flächen und ebene diskontinuierliche Gruppen*, Lecture Notes in Mathematics, Vol. 122, Springer-Verlag, Berlin-New York, 1970 (German). MR**0262378**

*Isotopie von Kurven auf orientierbaren geschlossenen Zweiseitigen Flächen*, Acta Math.

**50**(1927), Satz 11, 266.

*An involution of a closed*3-

*manifold with a tame fixed point set is*PL (to appear).

*Failure of Nielsen’s theorem in higher dimensions*(to appear).

## Bibliographic Information

- © Copyright 1976 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**223**(1976), 223-234 - MSC: Primary 57A10; Secondary 55A10
- DOI: https://doi.org/10.1090/S0002-9947-1976-0431177-0
- MathSciNet review: 0431177