Volume 3, issue 1 (1999)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
An elementary approach to the mapping class group of a surface

Bronisław Wajnryb

Geometry & Topology 3 (1999) 405–466

arXiv: math.GT/9912248

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
mapping class group, surface, curve complex, group presentation
Mathematical Subject Classification
Primary: 20F05, 20F34, 57M05
Secondary: 20F38, 57M60
References
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Publication
Received: 7 January 1999
Revised: 18 November 1999
Accepted: 6 December 1999
Published: 17 December 1999
Proposed: Joan Birman
Seconded: Walter Neumann, Cameron Gordon
Authors
Bronisław Wajnryb
Department of Mathematics
Technion
32000 Haifa
Israel