Topology
The extended mapping class group is generated by 3 symmetries
Comptes Rendus. Mathématique, Volume 338 (2004) no. 5, pp. 403-406.

We prove that for g⩾1 the extended mapping class group is generated by three orientation reversing involutions.

Nous prouvons que pour chaque g⩾1 le groupe modulaire étendu est éngendré par trois involutions qui inversent l'orientation.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2003.12.028
Stukow, Michał 1

1 Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland
@article{CRMATH_2004__338_5_403_0,
     author = {Stukow, Micha{\l}},
     title = {The extended mapping class group is generated by 3 symmetries},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {403--406},
     publisher = {Elsevier},
     volume = {338},
     number = {5},
     year = {2004},
     doi = {10.1016/j.crma.2003.12.028},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2003.12.028/}
}
TY  - JOUR
AU  - Stukow, Michał
TI  - The extended mapping class group is generated by 3 symmetries
JO  - Comptes Rendus. Mathématique
PY  - 2004
SP  - 403
EP  - 406
VL  - 338
IS  - 5
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2003.12.028/
DO  - 10.1016/j.crma.2003.12.028
LA  - en
ID  - CRMATH_2004__338_5_403_0
ER  - 
%0 Journal Article
%A Stukow, Michał
%T The extended mapping class group is generated by 3 symmetries
%J Comptes Rendus. Mathématique
%D 2004
%P 403-406
%V 338
%N 5
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2003.12.028/
%R 10.1016/j.crma.2003.12.028
%G en
%F CRMATH_2004__338_5_403_0
Stukow, Michał. The extended mapping class group is generated by 3 symmetries. Comptes Rendus. Mathématique, Volume 338 (2004) no. 5, pp. 403-406. doi : 10.1016/j.crma.2003.12.028. http://www.numdam.org/articles/10.1016/j.crma.2003.12.028/

[1] Birman, J. Automorphisms of the fundamental group of a closed, orientable 2-manifold, Proc. Amer. Math. Soc., Volume 21 (1969), pp. 351-354

[2] Birman, J.; Hilden, H. On mapping class groups of closed surfaces as covering spaces, Advances in the Theory of Riemann Surfaces, Ann. of Math. Stud., vol. 66, Princeton University Press, Princeton, NJ, 1971, pp. 81-115

[3] T. Brendle, B. Farb, Every mapping class group is generated by 3 torsion elements and by 7 involutions, Preprint 2003

[4] G. Gromadzki, M. Stukow, Involving symmetries of Riemann surfaces to a study of the mapping class group, Publ. Mat., in press

[5] Humphries, S. Generators for the mapping class group, Topology of Low-Dimensional Manifolds, Lecture Notes in Math., vol. 722, Springer, 1979, pp. 44-47

[6] Kerckhoff, S. The Nielsen realization problem, Ann. of Math., Volume 117 (1983), pp. 235-265

[7] M. Korkmaz, Generating the surface mapping class group by two elements, Preprint, 2003

[8] Maclachlan, C. Modulus space is simply-connected, Proc. Amer. Math. Soc., Volume 29 (1971), pp. 85-86

[9] Magnus, W.; Karass, A.; Solitar, D. Combinatorial Group Theory, Interscience, New York, 1966

[10] McCarthy, J.; Papadopoulos, A. Involutions in surface mapping class groups, Enseign. Math., Volume 33 (1987), pp. 275-290

[11] Wajnryb, B. Mapping class group of a surface is generated by two elements, Topology, Volume 35 (1996), pp. 377-383

[12] Wiman, A. Über die hyperelliptischen Kurven und diejenigen vom Geschlecht p=3, welche eindeutige Transformationen in sich zulassen, Bihang Till. Kongl. Svenska Vetenskaps-Akademiens Handl., Volume 21 (1895), pp. 1-23

Cited by Sources: