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Closed $ 3$-manifolds with no periodic maps


Authors: Frank Raymond and Jeffrey L. Tollefson
Journal: Trans. Amer. Math. Soc. 221 (1976), 403-418
MSC: Primary 57A10; Secondary 57E10
DOI: https://doi.org/10.1090/S0002-9947-1976-0415620-9
MathSciNet review: 0415620
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Abstract: Examples of closed, orientable, aspherical 3-manifolds are constructed on which every action of a finite group is trivial.


References [Enhancements On Off] (What's this?)

  • [1] J. S. Birman and H. M. Hilden, On isotopies of homeomorphisms of Riemann surfaces, Ann. of Math. (2) 97 (1973), 424-439. MR 48 #4305. MR 0325959 (48:4305)
  • [2] E. Bloomberg, Manifolds with no periodic maps, Trans. Amer. Math. Soc. 202 (1975), 67-78. MR 0358842 (50:11301)
  • [3] A. Borel, Seminar on transformation groups, Ann. of Math. Studies, no. 46, Princeton Univ. Press, Princeton, N. J., 1960, p. 38. MR 22 #7129. MR 0116341 (22:7129)
  • [4] P. E. Conner and F. Raymond, Manifolds with few periodic homeomorphisms, Proc. Second Conf. on Compact Transformation Groups (Amherst, Mass., 1971), part II, Springer-Verlag, New York, 1972, pp. 1-75. MR 0358835 (50:11294)
  • [5] P. E. Conner, F. Raymond and P. Weinberger, Manifolds with no periodic maps, Proc. Second Conf. on Compact Transformation Groups (Amherst, Mass., 1971), part II, Springer-Verlag, New York, 1972, pp. 81-108. MR 0358836 (50:11295)
  • [6] D. B. A. Epstein, Curves on 2-manifolds and isotopies, Acta Math. 115 (1966), 83-107. MR 35 #4938. MR 0214087 (35:4938)
  • [7] K. W. Kwun and J. L. Tollefson, PL involutions of $ {S^1} \times {S^1} \times {S^1}$, Trans. Amer. Math. Soc. 203 (1975), 97-106. MR 0370634 (51:6861)
  • [8] W. B. R. Lickorisch, A representation of orientable combinatorial 3-manifolds, Ann. of Math. (2) 76 (1962), 531-540. MR 27 #1929. MR 0151948 (27:1929)
  • [9] J. Nielsen, Abbildungsklassen endlicher Ordnung, Acta Math. 75 (1942), 23-115. MR 7, 137. MR 0013306 (7:137a)
  • [10] J. L. Tollefson, A 3-manifold with no PL involutions, Notices Amer. Math. Soc. 22 (1975), A-231. Abstract #720-57-13.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1976-0415620-9
Keywords: Periodic maps, 3-manifolds
Article copyright: © Copyright 1976 American Mathematical Society

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