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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Generating the surface mapping class group by two elements


Author: Mustafa Korkmaz
Journal: Trans. Amer. Math. Soc. 357 (2005), 3299-3310
MSC (2000): Primary 57M07, 20F05; Secondary 57M60, 20F38
Published electronically: December 28, 2004
MathSciNet review: 2135748
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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.


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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: http://dx.doi.org/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
Published electronically: 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-GEBİP 2003-10)
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.