Connectedness of nonseparating disk pants graph of a handlebody

In this paper, we introduce the definition of nonseparating disk pants graph for a handlebody, and prove that for [Formula: see text], the nonseparating disk pants graph is connected.

Exhausting pants graphs of punctured spheres by finite rigid sets

Let [Formula: see text] be an [Formula: see text]-punctured sphere. For [Formula: see text], we construct a sequence [Formula: see text] of finite rigid sets in the pants graph [Formula: see text] such that [Formula: see text] and [Formula: see text].

Connectivity of certain simplicial complexes associated to a handlebody

In this paper, we prove three simplicial complexes associate to a handlebody, which are separating disk complex, half disk complex and disk pants graph, are connected.

Products of Farey graphs are totally geodesic in the pants graph

We show that for a surface [Formula: see text], the subgraph of the pants graph determined by fixing a collection of curves that cut [Formula: see text] into pairs of pants, once-punctured tori, and four-times-punctured spheres is totally geodesic. The main theorem resolves a special case of a conjecture made in [2] and has the implication that an embedded product of Farey graphs in any pants graph is totally geodesic. In addition, we show that a pants graph contains a convex [Formula: see text]-flat if and only if it contains an [Formula: see text]-quasi-flat.

Prescribing the behavior of Weil–Petersson geodesics in the moduli space of Riemann surfaces

We study Weil–Petersson (WP) geodesics with narrow end invariant and develop techniques to control length-functions and twist parameters along them and prescribe their itinerary in the moduli space of Riemann surfaces. This class of geodesics is rich enough to provide for examples of closed WP geodesics in the thin part of the moduli space, as well as divergent WP geodesic rays with minimal filling ending lamination. Some ingredients of independent interest are the following: A strength version of Wolpert's Geodesic Limit Theorem proved in Sec. 4. The stability of hierarchy resolution paths between narrow pairs of partial markings or laminations in the pants graph proved in Sec. 5. A kind of symbolic coding for laminations in terms of subsurface coefficients presented in Sec. 7.