Advertisement

Inventiones mathematicae

, Volume 86, Issue 2, pp 287–346 | Cite as

Finite group actions on 3-manifolds

  • William H. MeeksIII
  • Peter Scott
Article

Keywords

Group Action Finite Group Finite Group Action 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [Bi] Bing, R.H.: A homeomorphism between the 3-sphere and the sum of two solid horned spheres. Ann. Math.56, 354–362 (1952)Google Scholar
  2. [B-N] Bundgard, S., Nielsen, J.: On normal subgroups with finite index inF-groups. Mat. Tidsskr. B 56–58 (1951)Google Scholar
  3. [C-F] Cannon, J.W., Feustel, C.D.: Essential annuli and Moebius bands inM 3. Trans. Am. Math. Soc.215, 219–236 (1976)Google Scholar
  4. [E-L] Edmonds, A.L., Livingston, C.: Group actions on fibered 3-manifolds. Comment. Math. Helv.58, 529–542 (1983)Google Scholar
  5. [Ei] Eilenberg, S.: Sur les transformations périodiques de la surface du sphère. Fundam. Math.22, 28–41 (1934)Google Scholar
  6. [Ep] Epstein, D.B.A.: Projective planes in 3-manifolds. Proc. Lond. Math. Soc.11, 469–484 (1961)Google Scholar
  7. [Feu 1] Feustel, C.D.: On the torus theorem and its applications. Trans. Am. Math. Soc.217, 1–43 (1976)Google Scholar
  8. [Feu 2] Feustel, C.D.: On the torus theorem for closed 3-manifolds. Trans. Am. Math. Soc.217, 45–57 (1976)Google Scholar
  9. [Fox] Fox, R.H.: On Fenchel's conjecture aboutF-groups. Mat. Tidsskr. B 61–65 (1952)Google Scholar
  10. [FHS] Freedman, M., Hass, J., Scott, P.: Least area incompressible surfaces in 3-manifolds. Invent. Math.71, 609–642 (1983)Google Scholar
  11. [F-Y] Freedman, M., Yau, S.-T.: Homotopically trivial symmetries of Haken manifolds are toral. Topology22, 179–189 (1983)Google Scholar
  12. [H] Hempel, J.: Free cyclic actions onS 1×S 1×S 1. Proc. Am. Math. Soc.48, 221–227 (1975)Google Scholar
  13. [J-S] Jaco, W., Shalen, P.B.: Seifert fibered spaces in 3-manifolds. Mem. Am. Math. Soc.220 (1979)Google Scholar
  14. [Jo] Johannson, K.: Homotopy equivalences of 3-manifolds with boundary. Lect. Notes Math.761 (1979)Google Scholar
  15. [Ke] Kerckhoff, S.P.: The Nielsen realisation problem. Ann. Math.117, 235–265 (1983)Google Scholar
  16. [K-T] Kim, P., Tollefson, J.: PL involutions of fibered manifolds. Trans. Am. Math. Soc.232, 221–237 (1977)Google Scholar
  17. [Kw-T1] Kwun, K., Tollefson, J.: PL involutions ofS 1×S 1×S 1. Trans. Am. Math. Soc.203, 97–106 (1975)Google Scholar
  18. [Kw-T2] Kwun, K., Tollefson, J.: Extending a PL involution of the interior of a compact manifold. Am. J. Math.99, 995–1001 (1977)Google Scholar
  19. [L] Lemaire, L.: Boundary value problems for harmonic and minimal maps of surfaces into manifolds. Ann. Sc. Norm. Super. Pisa9, 91–103 (1982)Google Scholar
  20. [Liv] Livesay, G.R.: Involutions with two fixed points on the three-sphere. Ann. Math.78, 582–593 (1963)Google Scholar
  21. [M-Y1] Meeks, W.H., Yau, S.-T.: Topology of three dimensional manifolds and the embedding problems in minimal surface theory. Ann. Math.112, 441–485 (1980)Google Scholar
  22. [M-Y2] Meeks, W.H., Yau, S.-T.: The equivariant Dehn's Lemma and Loop Theorem. Comment. Math. Helv.56, 225–239 (1981)Google Scholar
  23. [M-Y3] Meeks, W.H., Yau, S.-T.: Group actions on ℝ3. In: Morgan, Bass (eds): The Smith conjecture. New York: Academic Press 1984, pp. 167–179Google Scholar
  24. [Mi] Miller, R.T.: A new proof of the homotopy torus and annulus theorems. (preprint, Michigan State University, East Lansing, Michigan 48824)Google Scholar
  25. [O-R] Orlik, P., Raymond, F.: On 3-manifolds with localSO(2) action. Q. J. Math., Oxf.20, 143–160 (1969)Google Scholar
  26. [O-V-Z] Orlik, P., Vogt, E., Zieschang, H.: Zur Topologie gefaserter dreidimensionaler Mannigfaltigkeiten. Topology6, 49–64 (1967)Google Scholar
  27. [Ru1] Rubinstein, J.H.: Heegaard splittings and a theorem of Livesay. Proc. Am. Math. Soc.60, 317–320 (1976)Google Scholar
  28. [Ru2] Rubinstein, J.H.: Free actions of some finite groups onS 3. Math. Ann.240, 165–175 (1979)Google Scholar
  29. [S-U] Sacks, J., Uhlenbeck, K.: The existence of minimal immersions of 2-spheres. Ann. Math.113, 1–24 (1981)Google Scholar
  30. [S-Y] Schoen, R., Yau, S.-T.: Existence of incompressible minimal surfaces and the topology of three dimensional manifolds with non-negative scalar curvature. Ann. Math.110, 127–142 (1979)Google Scholar
  31. [Sc1] Scott, P.: Subgroups of surface groups are almost geometric. J. Lond. Math. Soc.17, 555–565 (1978)Google Scholar
  32. [Sc2] Scott, P.: A new proof of the Annulus and Torus Theorems. Am. J. Math.102, 241–277 (1980)Google Scholar
  33. [Sc3] Scott, P.: There are no fake Seifert fibre spaces with infinite π1. Ann. Math.117, 35–70 (1983)Google Scholar
  34. [Sc4] Scott, P.: The geometries of 3-manifolds. Bull. Lond. Math. Soc.15, 401–487 (1983)Google Scholar
  35. [Sel] Selberg, A.: On discontinuous groups in higher dimensional symmetric spaces. Contributions to function theory (Bombay, 1960), pp. 147–164Google Scholar
  36. [SCP] The Smith conjecture (eds: Morgan and Bass), New York: Academic Press 1984Google Scholar
  37. [Th1] Thurston, W.P.: The geometry and topology of 3-manifolds. (to be published by Princeton University Press)Google Scholar
  38. [Th2] Thurston, W.P.: Hyperbolic geometry and 3-manifolds, Low-dimensional topology. Lect. Notes Ser. (eds: Brown and Thickstun)48, Cambridge University Press, London Math. Soc. 1982, pp. 9–25Google Scholar
  39. [Th3] Thurston, W.P.: Three-dimensional manifolds, Kleinian groups and hyperbolic geometry. Bull. Am. Math. Soc.6, 357–381 (1982)Google Scholar
  40. [Th4] Thurston, W.P.: Three-manifolds with symmetry (preprint)Google Scholar
  41. [To1] Tollefson, J.: Homotopically trivial periodic homeomorphisms of 3-manifolds. Ann. Math.97, 14–26 (1973)Google Scholar
  42. [To2] Tollefson, J.: Involutions of Seifert fibre spaces. Pac. J. Math.74, 519–529 (1978)Google Scholar
  43. [W] Wolf, J.A.: Spaces of constant curvature. McGraw-Hill, New York, 1967Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • William H. MeeksIII
    • 1
  • Peter Scott
    • 1
  1. 1.Pure Mathematics DepartmentThe University of LiverpoolLiverpoolUK

Personalised recommendations