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Large flats in the pants graph
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.Comment: 16 pages, 3 figure
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