Train track complex of once-punctured torus and 4-punctured sphere

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dc.creatorIbaraki, Keita
dc.date2009-01-07
dc.date.accessioned2026-07-07T12:27:07Z
dc.date.available2026-07-07T12:27:07Z
dc.descriptionConsider a compact oriented surface $S$ of genus $g \geq 0$ and $m \geq 0$ punctured. The train track complex of $S$ which is defined by Hamenstädt is a 1-complex whose vertices are isotopy classes of complete train tracks on $S$. Hamenstädt shows that if $3g-3+m \geq 2$, the mapping class group acts properly discontinuously and cocompactly on the train track complex. We will prove corresponding results for the excluded case, namely when $S$ is a once-punctured torus or a 4-punctured sphere. To work this out, we redefinition of two complexes for these surfaces.
dc.description19 pages, 13 figures
dc.identifierhttps://arxiv.org/abs/0901.0747
dc.identifierhttp://arxiv.org/abs/0901.0747
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/215103
dc.subjectGeneral Topology
dc.subjectAlgebraic Geometry
dc.subject57M60
dc.titleTrain track complex of once-punctured torus and 4-punctured sphere
dc.typetext

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