[Le groupe modulaire hyperelliptique d'une surface non orientable de genre g ≥ 4 a une représentation fidèle dans ]
We prove that the hyperelliptic mapping class group of a nonorientable surface of genus has a faithful linear representation of dimension over .
Nous démontrons que le groupe modulaire hyperelliptique d'une surface non orientable de genre a une représentation fidèle linéaire de dimension sur .
Accepté le :
Publié le :
Stukow, Michał 1
@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},
year = {2016},
publisher = {Elsevier},
volume = {354},
number = {10},
doi = {10.1016/j.crma.2016.07.015},
language = {en},
url = {https://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 - https://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
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%N 10
%I Elsevier
%U https://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
[1] Braid groups are linear, J. Amer. Math. Soc., Volume 14 (2001) no. 2, pp. 471-486
[2] The mapping class group of a genus two surface is linear, Algebraic Geom. Topol., Volume 1 (2001), pp. 699-708
[3] On the homeotopy group of a non-orientable surface, Math. Proc. Camb. Philos. Soc., Volume 71 (1972), pp. 437-448
[4] The hyperelliptic mapping class group of Klein surfaces, Proc. Edinb. Math. Soc., Volume 44 (2001) no. 2, pp. 351-363
[5] Hyperelliptic Klein surfaces, Quart. J. Math. Oxford, Volume 36 (1985) no. 2, pp. 141-157
[6] On the linearity of certain mapping class groups, Turk. J. Math., Volume 24 (2000) no. 4, pp. 367-371
[7] Braid groups are linear, Ann. Math., Volume 155 (2002) no. 1, pp. 131-156
[8] The complex of curves on non-orientable surfaces, J. Lond. Math. Soc., Volume 25 (1982) no. 2, pp. 171-184
[9] Conjugacy classes of finite subgroups of certain mapping class groups, Turk. J. Math., Volume 28 (2004) no. 2, pp. 101-110
[10] A finite presentation for the hyperelliptic mapping class group of a nonrientable surface, Osaka J. Math., Volume 52 (2015) no. 2, pp. 495-515
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