Large flats in the pants graph
Geometric Topology
2013-06-14 v1
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.
Cite
@article{arxiv.1306.3170,
title = {Large flats in the pants graph},
author = {José L. Estévez},
journal= {arXiv preprint arXiv:1306.3170},
year = {2013}
}
Comments
16 pages, 3 figures