Simplicial embeddings between multicurve graphs

Abstract

We study some graphs associated to a surface, called k-multicurve graphs, which interpolate between the curve complex and the pants graph. Our main result is that, under certain conditions, simplicial embeddings between multicurve graphs are induced by ${\pi }_1$-injective embeddings of the corresponding surfaces. We also prove the rigidity of the multicurve graphs.

arXiv commentNew introduction and some changes in Section 2, main results unchanged. References added. 18 pages, 5 figures