Mapping class groups of non-orientable surfaces for beginners

Luis Paris[1]

  • [1] Université de Bourgogne, Institut de Mathématiques de Bourgogne, UMR 5584 du CNRS, B.P. 47870, 21078 Dijon cedex, France.

Winter Braids Lecture Notes (2014)

  • Volume: 1, page 1-17
  • ISSN: ?? -

Abstract

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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.

How to cite

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Paris, Luis. "Mapping class groups of non-orientable surfaces for beginners." Winter Braids Lecture Notes 1 (2014): 1-17. <http://eudml.org/doc/275815>.

@article{Paris2014,
abstract = {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.},
affiliation = {Université de Bourgogne, Institut de Mathématiques de Bourgogne, UMR 5584 du CNRS, B.P. 47870, 21078 Dijon cedex, France.},
author = {Paris, Luis},
journal = {Winter Braids Lecture Notes},
language = {eng},
pages = {1-17},
publisher = {Winter Braids School},
title = {Mapping class groups of non-orientable surfaces for beginners},
url = {http://eudml.org/doc/275815},
volume = {1},
year = {2014},
}

TY - JOUR
AU - Paris, Luis
TI - Mapping class groups of non-orientable surfaces for beginners
JO - Winter Braids Lecture Notes
PY - 2014
PB - Winter Braids School
VL - 1
SP - 1
EP - 17
AB - 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.
LA - eng
UR - http://eudml.org/doc/275815
ER -

References

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  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. Zbl0232.57001MR300288
  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. Zbl0217.48602MR292082
  3. D. B. A. Epstein. Curves on 2 -manifolds and isotopies. Acta Math. 115 (1966), 83–107. Zbl0136.44605MR214087
  4. B. Farb, D. Margalit. A primer on mapping class groups. Princeton Mathematical Series, 49. Princeton University Press, Princeton, NJ, 2012. Zbl1245.57002MR2850125
  5. A. Fathi, F. Laudenbach, V. Poénaru. Travaux de Thurston sur les surfaces. Séminaire Orsay. Astérisque, 66–67. Société Mathématique de France, Paris, 1979. Zbl0446.57010MR568308
  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. Zbl0883.57016MR1435728
  8. N. V. Ivanov. Automorphisms of complexes of curves and of Teichmüller spaces. Internat. Math. Res. Notices 1997, no. 14, 651–666. Zbl0890.57018MR1460387
  9. M. Korkmaz. Mapping class groups of nonorientable surfaces. Geom. Dedicata 89 (2002), 109–133. Zbl1016.57013MR1890954
  10. W. B. R. Lickorish. Homeomorphisms of non-orientable two-manifolds. Proc. Cambridge Philos. Soc. 59 (1963), 307–317. Zbl0115.40801MR145498
  11. L. Paris, D. Rolfsen. Geometric subgroups of mapping class groups. J. Reine Angew. Math. 521 (2000), 47–83. Zbl1007.57014MR1752295
  12. M. Stukow. Dehn twists on nonorientable surfaces. Fund. Math. 189 (2006), no. 2, 117–147. Zbl1101.57008MR2214574
  13. M. Stukow. Commensurability of geometric subgroups of mapping class groups. Geom. Dedicata 143 (2009), 117–142. Zbl1195.57043MR2576298
  14. M. Stukow. Subgroup generated by two Dehn twists on nonorientable surface. Preprint, arXiv:1310.3033. Zbl1101.57008
  15. Wu Yingqing. Canonical reducing curves of surface homeomorphism. Acta Math. Sinica (N.S.) 3 (1987), no. 4, 305–313. Zbl0651.57008MR930761
  16. H. Zieschang. On the homeotopy group of surfaces. Math. Ann. 206 (1973), 1–21. Zbl0248.55001MR335794

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