English

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.

Keywords

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

R2 v1 2026-06-22T00:33:26.901Z