English

An elementary approach to the mapping class group of a surface

Geometric Topology 2014-11-11 v1

Abstract

We consider an oriented surface S and a cellular complex X of curves on S, defined by Hatcher and Thurston in 1980. We prove by elementary means, without Cerf theory, that the complex X is connected and simply connected. From this we derive an explicit simple presentation of the mapping class group of S, following the ideas of Hatcher-Thurston and Harer.

Keywords

Cite

@article{arxiv.math/9912248,
  title  = {An elementary approach to the mapping class group of a surface},
  author = {Bronislaw Wajnryb},
  journal= {arXiv preprint arXiv:math/9912248},
  year   = {2014}
}

Comments

62 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol3/paper17.abs.html

R2 v1 2026-07-22T18:06:07.023Z