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Products of Farey graphs are totally geodesic in the pants graph
Taylor, SJ Zupan, A
Taylor, SJ
Zupan, A
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Journal Article
Date
2016-06-01
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10.1142/S1793525316500096
Abstract
© 2016 World Scientific Publishing Company. We show that for a surface ∑, the subgraph of the pants graph determined by fixing a collection of curves that cut ∑ into pairs of pants, once-punctured tori, and four-times-punctured spheres is totally geodesic. The main theorem resolves a special case of a conjecture made in [2] and has the implication that an embedded product of Farey graphs in any pants graph is totally geodesic. In addition, we show that a pants graph contains a convex n-flat if and only if it contains an n-quasi-flat.
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World Scientific Pub Co Pte Lt
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Journal of Topology and Analysis
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