Mapping Class Factorization via Fatgraph Nielsen Reduction

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dc.creatorBene, Alex James
dc.date2009-04-27
dc.date.accessioned2026-07-07T13:08:53Z
dc.date.available2026-07-07T13:08:53Z
dc.descriptionThe mapping class group of a genus $g$ surface $Σ_{g,1}$ with one boundary component is known to have a simple yet infinite presentation with generators given by elementary moves called Whitehead moves on so-called marked bordered fatgraphs. In this paper, we introduce an algorithm called "fatgraph Nielsen reduction" which, from the action of a mapping class $φ\in MC_{g,1}$ of $Σ_{g,1}$ on the fundamental group $π_1(Σ_{g,1})$ of $Σ_{g,1}$, determines a sequence of Whitehead moves representing $φ$ beginning at any choice of marked bordered fatgraph. As a consequence, this leads to an algorithm which factors any mapping class given by its action on $π(Σ_{g,1})$ in terms of a certain generating set for $MC_{g,1}$.
dc.description16 pages, 4 figures
dc.identifierhttps://arxiv.org/abs/0904.4067
dc.identifierhttp://arxiv.org/abs/0904.4067
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/228565
dc.subjectGeometric Topology
dc.subject20F38; 05C25; 20F34; 57M99; 32G15; 20F05; 20F06; 20F99
dc.titleMapping Class Factorization via Fatgraph Nielsen Reduction
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