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29 March 2024
 
  » arxiv » 1306.3170

 Article overview


Large flats in the pants graph
José L. Estévez ;
Date 13 Jun 2013
AbstractThis 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.
Source arXiv, 1306.3170
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