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Generating the surface mapping class group by two elements
Author(s):
Mustafa
Korkmaz
Journal:
Trans. Amer. Math. Soc.
357
(2005),
3299-3310.
MSC (2000):
Primary 57M07, 20F05;
Secondary 57M60, 20F38
Posted:
December 28, 2004
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Abstract:
Wajnryb proved in 1996 that the mapping class group of an orientable surface is generated by two elements. We prove that one of these generators can be taken as a Dehn twist. We also prove that the extended mapping class group is generated by two elements, again one of which is a Dehn twist. Another result we prove is that the mapping class groups are also generated by two elements of finite order.
References:
-
- 1.
- T. Brendle, B. Farb, Every mapping class group is generated by
 involutions, J. Algebra 278 (2004), 187-198. MR 2068073 - 2.
- M. Dehn, Die gruppe der abdildungsklassen, Acta Math. 69 (1938), 135-206.
- 3.
- S. Humphries, Generators for the mapping class group, in: Topology of Low Dimensional Manifolds, Ed. by R. Fenn, Lecture Notes in Math. No. 722, Springer-Verlag, Berlin, 1979, 44-47. MR 80i:57010
- 4.
- D. L. Johnson, The structure of the Torelli group I: A finite set of generators for
 , Annals of Math. (2) 118 (1983), 423-442. MR 85a:57005 - 5.
- W. B. R. Lickorish, A representation of orientable combinatorial 3-manifolds, Annals of Mathematics 76 (1962), 531-540. MR 27:1929
- 6.
- W. B. R. Lickorish, A finite set of generators for the homeotopy group of a 2-manifold, Math. Proc. Camb. Phil. Soc. 60 (1964), 769-778. MR 30:1500
- 7.
- B. Wajnryb, A simple presentation for the mapping class group of an orientable surface, Israel Jounal of Mathematics 45 (1983), 157-174. MR 85g:57007
- 8.
- B. Wajnryb, Mapping class group of a surface is generated by two elements, Topology 35 (1996), 377-383. MR 96m:57007
- 9.
- B. Wajnryb, An elementary approach to the mapping class group of a surface, Geom. Topol. 3 (1999), 405-466. MR 2001a:20059
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Additional Information:
Mustafa
Korkmaz
Affiliation:
Department of Mathematics, Middle East Technical University, 06531 Ankara, Turkey
Email:
korkmaz@arf.math.metu.edu.tr
DOI:
10.1090/S0002-9947-04-03605-0
PII:
S 0002-9947(04)03605-0
Received by editor(s):
November 8, 2003
Received by editor(s) in revised form:
January 8, 2004
Posted:
December 28, 2004
Additional Notes:
The author was supported in part by the Turkish Academy of Sciences under the Young Scientists Award Program (MK/TÜBA-GEBIP 2003-10)
Copyright of article:
Copyright
2004,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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