We prove that the word problem in the mapping class group of the once-punctured surface of genus g has complexity O(|w| 2 g) for |w| log(g) where |w| is the length of the word in a (standard) set of generators. The corresponding bound in the case of the closed surface is O(|w| 2 g 2 ). We also carry
The mapping class group and a theorem of Masur–Wolf
✍ Scribed by John D. McCarthy; Athanase Papadopoulos
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 96 KB
- Volume
- 96
- Category
- Article
- ISSN
- 0166-8641
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✦ Synopsis
In (Masur and Wolf, 1995), Masur and Wolf proved that the Teichmüller space of genus g > 1 surfaces with the Teichmüller metric is not a Gromov hyperbolic space. In this paper, we provide an alternative proof based upon a study of the action of the mapping class group on Teichmüller space.
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Partially supported by the research funds of Ministero dell'Uni¨ersita e della Ricerca Scientifica e Tecnologica and by Grant 9300856.CT01 of Consiglio Nazionale delle Ricerche.
We study representations of subgroups of the mapping class group M g of a surface of genus g 2 arising from the actions of them on the first cohomology groups of the surface with local coefficient systems which are defined by nontrivial homomorphisms π 1 (Σ g , \* ) → Z 2 = Aut(Z). As an application