no. 10
Topology
The hyperelliptic mapping class group of a nonorientable surface of genus g ≥ 4 has a faithful representation into GL(g2−1,R)
[Le groupe modulaire hyperelliptique d'une surface non orientable de genre g ≥ 4 a une représentation fidèle dans GL(g2−1,R)]

Présenté par : the Editorial Board

Stukow, Michał1
1 Institute of Mathematics, Faculty of Mathematics, Physics and Informatics, University of Gdańsk, 80-308 Gdańsk, Poland
Comptes Rendus. Mathématique, Tome 354 (2016) no. 10, pp. 1029-1031.

Nous démontrons que le groupe modulaire hyperelliptique d'une surface non orientable de genre g≥4 a une représentation fidèle linéaire de dimension g2−1 sur R.

We prove that the hyperelliptic mapping class group of a nonorientable surface of genus g≥4 has a faithful linear representation of dimension g2−1 over R.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2016.07.015
Stukow, Michał 1

1 Institute of Mathematics, Faculty of Mathematics, Physics and Informatics, University of Gdańsk, 80-308 Gdańsk, Poland 
@article{CRMATH_2016__354_10_1029_0,
     author = {Stukow, Micha{\l}},
     title = {The hyperelliptic mapping class group of a nonorientable surface of genus \protect\emph{g}\,\ensuremath{\geq}\,4 has a faithful representation into $ \mathrm{GL}({g}^{2}-1,\mathbb{R})$},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1029--1031},
     publisher = {Elsevier},
     volume = {354},
     number = {10},
     year = {2016},
     doi = {10.1016/j.crma.2016.07.015},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2016.07.015/}
}
TY  - JOUR
AU  - Stukow, Michał
TI  - The hyperelliptic mapping class group of a nonorientable surface of genus g ≥ 4 has a faithful representation into $ \mathrm{GL}({g}^{2}-1,\mathbb{R})$
JO  - Comptes Rendus. Mathématique
PY  - 2016
SP  - 1029
EP  - 1031
VL  - 354
IS  - 10
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2016.07.015/
DO  - 10.1016/j.crma.2016.07.015
LA  - en
ID  - CRMATH_2016__354_10_1029_0
ER  - 
%0 Journal Article
%A Stukow, Michał
%T The hyperelliptic mapping class group of a nonorientable surface of genus g ≥ 4 has a faithful representation into $ \mathrm{GL}({g}^{2}-1,\mathbb{R})$
%J Comptes Rendus. Mathématique
%D 2016
%P 1029-1031
%V 354
%N 10
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2016.07.015/
%R 10.1016/j.crma.2016.07.015
%G en
%F CRMATH_2016__354_10_1029_0
Stukow, Michał. The hyperelliptic mapping class group of a nonorientable surface of genus g ≥ 4 has a faithful representation into $ \mathrm{GL}({g}^{2}-1,\mathbb{R})$. Comptes Rendus. Mathématique, Tome 354 (2016) no. 10, pp. 1029-1031. doi : 10.1016/j.crma.2016.07.015. http://www.numdam.org/articles/10.1016/j.crma.2016.07.015/

[1] Bigelow, S.J. Braid groups are linear, J. Amer. Math. Soc., Volume 14 (2001) no. 2, pp. 471-486

[2] Bigelow, S.J.; Budney, R.D. The mapping class group of a genus two surface is linear, Algebraic Geom. Topol., Volume 1 (2001), pp. 699-708

[3] Birman, J.S.; Chillingworth, D.R.J. On the homeotopy group of a non-orientable surface, Math. Proc. Camb. Philos. Soc., Volume 71 (1972), pp. 437-448

[4] Bujalance, E.; Costa, A.F.; Gamboa, J.M. The hyperelliptic mapping class group of Klein surfaces, Proc. Edinb. Math. Soc., Volume 44 (2001) no. 2, pp. 351-363

[5] Bujalance, E.; Etayo, J.J.; Gamboa, J.M. Hyperelliptic Klein surfaces, Quart. J. Math. Oxford, Volume 36 (1985) no. 2, pp. 141-157

[6] Korkmaz, M. On the linearity of certain mapping class groups, Turk. J. Math., Volume 24 (2000) no. 4, pp. 367-371

[7] Kramer, D. Braid groups are linear, Ann. Math., Volume 155 (2002) no. 1, pp. 131-156

[8] Scharlemann, M. The complex of curves on non-orientable surfaces, J. Lond. Math. Soc., Volume 25 (1982) no. 2, pp. 171-184

[9] Stukow, M. Conjugacy classes of finite subgroups of certain mapping class groups, Turk. J. Math., Volume 28 (2004) no. 2, pp. 101-110

[10] Stukow, M. A finite presentation for the hyperelliptic mapping class group of a nonrientable surface, Osaka J. Math., Volume 52 (2015) no. 2, pp. 495-515

Cité par Sources :