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A combinatorial algorithm to compute presentations of mapping class groups of orientable surfaces with one boundary component

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Published/Copyright: September 26, 2015
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Abstract

We give an algorithm which computes a presentation for a subgroup, denoted 𝒜ℳg,p,1, of the automorphism group of a free group. It is known that 𝒜ℳg,p,1 is isomorphic to the mapping class group of an orientable genus-g surface with p punctures and one boundary component. We define a variation of the Auter space.

Funding source: MIC

Award Identifier / Grant number: MTM2008-01550

The author is grateful to Warren Dicks for introducing him to algebraic mapping class groups and to Luis Paris for his advices during a post-doc in Dijon. The article has been benefited by the anonymous referee's remarks.

Received: 2015-2-1
Published Online: 2015-9-26
Published in Print: 2015-11-1

© 2015 by De Gruyter

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