11 citations · 16 across the 8 of their papers we have counts for
9 papers
Convexity of strata in diagonal pants graphs of surfaces
Javier Aramayona, Cyril Lecuire, Hugo Parlier +1
We prove a number of convexity results for strata of the diagonal pants graph of a surface, in analogy with the extrinsic geometric properties of strata in the Weil-Petersson compl…
Constructing convex planes in the pants complex
Javier Aramayona, Hugo Parlier, Kenneth J. Shackleton
Our main theorem identifies a class of totally geodesic subgraphs of the 1-skeleton of the pants complex, each isomorphic to the product of two Farey graphs. We deduce the existenc…
On the distance between Seifert surfaces
Makoto Sakuma, Kenneth J. Shackleton
For a knot , Kakimizu introduced a simplicial complex whose vertices are all the isotopy classes of minimal genus spanning surfaces for . The first purpose of this paper is t…
Totally geodesic subgraphs of the pants complex
Javier Aramayona, Hugo Parlier, Kenneth J. Shackleton
Our main theorem asserts that every Farey graph embedded in the 1-skeleton of the pants complex of any finite type surface is totally geodesic.
Free subgroups of surface mapping class groups
James W. Anderson, Javier Aramayona, Kenneth J. Shackleton
We quantify the generation of free subgroups of surface mapping class groups by pseudo-Anosov mapping classes in terms of their translation distance and the distance between their…
Uniformly exponential growth and mapping class groups of surfaces
James W. Anderson, Javier Aramayona, Kenneth J. Shackleton
We show that the mapping class group of an orientable finite type surface has uniformly exponential growth, as well as various closely related groups. This provides further evidenc…