Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-29T03:30:19.735Z Has data issue: false hasContentIssue false
  • English
  • Français

A minimal generating set of the level 2 mapping class group of a non-orientable surface

Published online by Cambridge University Press:  30 July 2014

SUSUMU HIROSE  and
MASATOSHI SATO
SUSUMU HIROSE
Affiliation:
Department of Mathematics, Faculty of Science and Technology, Tokyo University of Science, Noda, Chiba, 278-8510, Japan e-mail: hirose_susumu@ma.noda.tus.ac.jp
MASATOSHI SATO
Affiliation:
Department of Mathematics Education, Faculty of Education, Gifu University, 1-1 Yanagito, Gifu, 501-1193, Japan e-mail: msato@gifu-u.ac.jp
Get access Rights & Permissions [Opens in a new window]

Abstract

We construct a minimal generating set of the level 2 mapping class group of a nonorientable surface of genus g, and determine its abelianization for g ≥ 4.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 157 , Issue 2 , September 2014 , pp. 345 - 355
Copyright
Copyright © Cambridge Philosophical Society 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Birman, J. S. and Chillingworth, D. R. J.On the homeotopy group of a non-orientable surface. Math. Proc. Camb. Phil. Soc. 71 (1972), 437–448. Erratum: Math. Proc. Camb. Phil. Soc. 136 (2004), 441–441.Google Scholar
[2]Bourbaki, N.Groupes et Algèbres de Lie. (Hermann, Paris, 1972), Ch. 2Google Scholar
[3]Broaddus, N., Farb, B. and Putman, A.Irreducible Sp-representations and subgroup distortion in the mapping class groups. Comm. Math. Helv. 86, no. 3 (2011), 537–556.Google Scholar
[4]Chillingworth, D. R. J.A finite set of generators for the homeotopy group of a non-orientable surface. Math. Proc. Camb. Phil. Soc. 65 (1969), 409–430.Google Scholar
[5]Johnson, D.An abelian quotient of the mapping class group $\Ncal{I_g}$. Math. Ann. 249 (1980), 225–242.Google Scholar
[6]Kawazumi, N. Cohomological aspects of Magnus expansions, preprint, math.GT/0505497 (2005).Google Scholar
[7]Korkmaz, M.First homology group of mapping class groups of nonorientable surfaces. Math. Proc. Camb. Phil. Soc. 123 (1998), 487–499.Google Scholar
[8]Lickorish, W. B. R.Homeomorphisms of non-orientable two-manifolds. Math. Proc. Camb. Phil. Soc. 59 (1963), 307–317.Google Scholar
[9]Lickorish, W. B. R.On the homeomorphisms of a non-orientable surface. Math. Proc. Camb. Phil. Soc. 61 (1965), 61–64.Google Scholar
[10]McCarthy, J. D. and Pinkall, U. Representing homology automorphisms of nonorientable surfaces. Max Planck Inst. Preprint MPI/SFB 85-11, revised version written on 26 Feb 2004, available from http://www.math.msu.edu/~mccarthy/publications/selected.papers.html.Google Scholar
[11]Perron, B.Filtration de Johnson et groupe de Torelli modulo p, p premier, C. R. Math. Acad. Sci. Paris 346, no. 11–12 (2008), 667–670.Google Scholar
[12]Sato, M.The abelianization of the level d mapping class group. J. Topology 3, no.4 (2010), 847–882.Google Scholar
[13]Szepietowski, B.Crosscap slides and the level 2 mapping class group of a nonorientable surface. Geom. Dedicata 160 (2012), 169–183.Google Scholar
[14]Szepietowski, B.A finite generating set for the level 2 mapping class group of a nonorientable surface. Kodai Math. J. 36 (2013), 1–14.Google Scholar