Large flats in the pants graph

José L. Estévez

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arXiv · 1306.3170

Large flats in the pants graph

José L. Estévez

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Abstract

This note is about the geometry of the pants graph P(S), a natural simplicial graph associated to a finite type topological surface S where vertices represents pants decompositions. The main result in this note ascserts that for a multicurve Q whose complement is a number of subsurfaces of complexity at most 1. We prove that the corresponding subgraph P(Q) is totally geodesic in P, previously considering this as a metric space assigning length one to each edge. A flat is a graph isomorphic to the Cayley graph of an abelian torsion free group of finite rank. As a consequence of the main theorem we make explicit the existence of maximal size flats (large flats) in the pants graph.

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José L. Estévez. 2013-06-13. Large flats in the pants graph. https://arxiv.org/abs/1306.3170

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