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Torsion and periods in some groups of homeomorphisms of the circle

Published online by Cambridge University Press:  24 October 2008

P. Greenberg
P. Greenberg
Affiliation:
Institut Fourier, BP 74, 38402 St Martin d'Heres Cedex, France
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Extract

If g is an element of torsion of a group G, its order o(g) is the least positive integer such that go(g) = e. Let OG = {o(g);g ∈ G}. If G is a group of homeomorphisms of a space X, and if g ∈ G, x ∈ X let q(g, x) denote the cardinality of the g-orbit {gnx}n∈Z of x.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 112 , Issue 1 , July 1992 , pp. 29 - 44
Copyright
Copyright © Cambridge Philosophical Society 1992

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References

REFERENCES

[1]Bleirer, S. and Casson, A.. Automorphisms of Surfaces after Nielsen and Thurston. London Math. Soc. Student Texts no. 9 (Cambridge University Press, 1990).Google Scholar
[2]Bieri, R. and Strebel, R.. Unpublished notes on groups of piecewise-linear homeomorphisms.Google Scholar
[3]Brown, K.. Finiteness Properties of Groups. J. Pure Appl. Algebra 44 (1987), 45–75.CrossRefGoogle Scholar
[4]Greenberg, P.. Classifying spaces for foliations with isolated singularities. Trans. Amer. Math. Soc. 304 (1987), 417–419.CrossRefGoogle Scholar
[5]Greenberg, P.. Pseudogroups from group actions. Amer. J. Math. 109 (1987), 893–906.CrossRefGoogle Scholar
[6]Greenberg, P.. Pseudogroups of C 1 piecewise projective homeomorphisms. Pacific J. Math. 129 (1987), 67–75.CrossRefGoogle Scholar
[7]Greenberg, P.. The Euler class for ‘piecewise”-groups, to appear.Google Scholar
[8]Greenberg, P.. Projective aspects of the Higman–Thompson group. Preprint.Google Scholar
[9]Ghys, E. and Sergiescu, V.. Sur un groupe remarquable de difféomorphismes du cercle. Comment. Math. Helv. 62 (1987), 185–239.CrossRefGoogle Scholar
[10]Haefliger, A.. Homotopy and integrability. In Manifolds–Amsterdam 1970, Lecture Notes in Math. vol. 107 (Springer-Verlag, 1971), pp. 133–163.Google Scholar
[11]Ott, M.. Gruppen von stückweise linearen Homömorphismen in der Ebene. Diplomarbeit, J. W. Goethe Universität, Frankfurt (1988).Google Scholar
[12]Shimura, G.. Introduction to the Arithmetic Theory of Automorphic Functions (Princeton University Press, 1971).Google Scholar