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A note on the normal subgroups of mapping class groups

Published online by Cambridge University Press:  24 October 2008

D. D. Long
Affiliation:
University of Southampton

Extract

0. If Fg is a closed, orientable surface of genus g, then the mapping class group of Fg is the group whose elements are orientation preserving self homeomorphisms of Fg modulo isotopy. We shall denote this group by Mg. Recall that a group is said to be linear if it admits a faithful representation as a group of matrices (where the entries for this purpose will be in some field).

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

REFERENCES

[1]Birman, J.. Braids, Links and Mapping Class Groups. Annals of Math. Studies no. 82 (Princeton University Press, 1974).Google Scholar
[2]Casson, A. J.. Automorphisms of Surfaces after Nielsen and Thurston. Lecture Notes (University of Texas, 1982).Google Scholar
[3]Fathi, A., Laudenbach, F. and Poenaru, V.. Travaux de Thurston sur les surfaces. Astérisque 66–67 (1979), 5282.Google Scholar
[4]Grossman, E. K.. On the residual finiteness of certain mapping class groups. J. London Math. Soc. (2) 9 (1974), 160164.CrossRefGoogle Scholar
[5]Lyndon, R. and Schupp, P.. Combinatorial Group Theory (Springer-Verlag, 1977).Google Scholar
[6]A, J. McCarthy.. ‘Tits-alternative’ for subgroups of mapping class groups. Thesis, M.I.T. 1983.Google Scholar
[7]Magnus, W. and Peluso, A.. On a theorem of V. I. Arnol'd. Comm. Pure Appl. Math. 22 (1969), 683692.CrossRefGoogle Scholar
[8]Papadopoulos, A.. Réseaux ferroviares, difféomorphismes pseudo-Anosov et automorphismes symplectiques de l'homologie d'une surface. Thèse de 3e cycle, Orsay.Google Scholar
[9]Penner, R.. Private communication.Google Scholar
[10]Platonov, V. P.. The Frattini subgroups and finite approximability. Soviet Math. Dokl. 7 (1966), 15571560.Google Scholar