Mapping class groups of non-orientable surfaces for beginners
[Mapping class groups of non-orientable surfaces for beginners]
Luis Paris1
1 Université de Bourgogne, Institut de Mathématiques de Bourgogne, UMR 5584 du CNRS, B.P. 47870, 21078 Dijon cedex, France.
Winter Braids Lecture Notes, Winter Braids IV (Dijon, 2014), Tome 1 (2014), Exposé no. 3, 17 p.

The present paper is the notes of a mini-course addressed mainly to non-experts. Its purpose is to provide a first approach to the theory of mapping class groups of non-orientable surfaces.

Publié le :
DOI : 10.5802/wbln.4
Luis Paris 1

1 Université de Bourgogne, Institut de Mathématiques de Bourgogne, UMR 5584 du CNRS, B.P. 47870, 21078 Dijon cedex, France. 
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Luis Paris. Mapping class groups of non-orientable surfaces for beginners. Winter Braids Lecture Notes, Winter Braids IV (Dijon, 2014), Tome 1 (2014), Exposé no. 3, 17 p. doi : 10.5802/wbln.4. https://proceedings.centre-mersenne.org/articles/10.5802/wbln.4/

[1] J. S. Birman, D. R. J. Chillingworth. On the homeotopy group of a non-orientable surface. Proc. Cambridge Philos. Soc. 71 (1972), 437–448. | DOI | MR | Zbl

[2] J. S. Birman, H. M. Hilden. On the mapping class groups of closed surfaces as covering spaces. Advances in the theory of Riemann surfaces (Proc. Conf., Stony Brook, N.Y., 1969), pp. 81–115. Ann. of Math. Studies, No. 66. Princeton Univ. Press, Princeton, N.J., 1971. | DOI

[3] D. B. A. Epstein. Curves on 2-manifolds and isotopies. Acta Math. 115 (1966), 83–107. | DOI | MR | Zbl

[4] B. Farb, D. Margalit. A primer on mapping class groups. Princeton Mathematical Series, 49. Princeton University Press, Princeton, NJ, 2012. | DOI | Zbl

[5] A. Fathi, F. Laudenbach, V. Poénaru. Travaux de Thurston sur les surfaces. Séminaire Orsay. Astérisque, 66–67. Société Mathématique de France, Paris, 1979.

[6] M. Gendulphe. Paysage systolique des surfaces hyperboliques de caractéristique -1. Preprint. Available at http://matthieu.gendulphe.com/Gendulphe-PaysageSystolique.pdf

[7] A. Ishida. The structure of subgroup of mapping class groups generated by two Dehn twists. Proc. Japan Acad. Ser. A Math. Sci. 72 (1996), no. 10, 240–241. | DOI | MR | Zbl

[8] N. V. Ivanov. Automorphisms of complexes of curves and of Teichmüller spaces. Internat. Math. Res. Notices 1997, no. 14, 651–666. | DOI | Zbl

[9] M. Korkmaz. Mapping class groups of nonorientable surfaces. Geom. Dedicata 89 (2002), 109–133. | Zbl

[10] W. B. R. Lickorish. Homeomorphisms of non-orientable two-manifolds. Proc. Cambridge Philos. Soc. 59 (1963), 307–317. | DOI | MR | Zbl

[11] L. Paris, D. Rolfsen. Geometric subgroups of mapping class groups. J. Reine Angew. Math. 521 (2000), 47–83. | DOI | MR | Zbl

[12] M. Stukow. Dehn twists on nonorientable surfaces. Fund. Math. 189 (2006), no. 2, 117–147. | DOI | MR | Zbl

[13] M. Stukow. Commensurability of geometric subgroups of mapping class groups. Geom. Dedicata 143 (2009), 117–142. | DOI | MR | Zbl

[14] M. Stukow. Subgroup generated by two Dehn twists on nonorientable surface. Preprint, arXiv:1310.3033. | Zbl

[15] Wu Yingqing. Canonical reducing curves of surface homeomorphism. Acta Math. Sinica (N.S.) 3 (1987), no. 4, 305–313. | DOI | MR | Zbl

[16] H. Zieschang. On the homeotopy group of surfaces. Math. Ann. 206 (1973), 1–21. | DOI | MR | Zbl

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