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Closed -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
MathSciNet review:
0415620
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Additional Information
Abstract: Examples of closed, orientable, aspherical 3-manifolds are constructed on which every action of a finite group is trivial.
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S. Birman and Hugh
M. Hilden, On isotopies of homeomorphisms of Riemann surfaces,
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Edward
M. Bloomberg, Manifolds with no periodic
homeomorphisms, Trans. Amer. Math. Soc. 202 (1975), 67–78.
MR
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G. Bredon, E. E. Floyd, D. Montgomery, R. Palais. Annals of Mathematics
Studies, No. 46, Princeton University Press, Princeton, N.J., 1960. MR 0116341
(22 #7129)
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P.
E. Conner and Frank
Raymond, Manifolds with few periodic homeomorphisms, (Univ.
Massachusetts, Amherst, Mass., 1971) Springer, Berlin, 1972,
pp. 1–75. Lecture Notes in Math., Vol. 299. MR 0358835
(50 #11294)
- [5]
P.
E. Conner, Frank
Raymond, and Peter
J. Weinberger, Manifolds with no periodic maps, (Univ.
Massachusetts, Amherst, Mass., 1971) Springer, Berlin, 1972,
pp. 81–108. Lecture Notes in Math., Vol. 299. MR 0358836
(50 #11295)
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D.
B. A. Epstein, Curves on 2-manifolds and isotopies, Acta Math.
115 (1966), 83–107. MR 0214087
(35 #4938)
- [7]
Kyung
Whan Kwun and Jeffrey
L. Tollefson, 𝑃𝐿 involutions of
𝑆¹×𝑆¹×𝑆¹, Trans. Amer. Math. Soc. 203 (1975), 97–106. MR 0370634
(51 #6861), http://dx.doi.org/10.1090/S0002-9947-1975-0370634-1
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W.
B. R. Lickorish, A representation of orientable combinatorial
3-manifolds, Ann. of Math. (2) 76 (1962),
531–540. MR 0151948
(27 #1929)
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Jakob
Nielsen, Abbildungsklassen endlicher Ordnung, Acta Math.
75 (1943), 23–115 (German). MR 0013306
(7,137a)
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J. L. Tollefson, A 3-manifold with no PL involutions, Notices Amer. Math. Soc. 22 (1975), A-231. Abstract #720-57-13.
- [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
, 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:
http://dx.doi.org/10.1090/S0002-9947-1976-0415620-9
PII:
S 0002-9947(1976)0415620-9
Keywords:
Periodic maps,
3-manifolds
Article copyright:
© Copyright 1976 American Mathematical Society
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