On volumes and filling collections of multicurves

Cremaschi, Tommaso; Rodrigurz-Migueles, Jose Andres und Yarmola, Andrew (2022): On volumes and filling collections of multicurves. In: Journal of Topology, Vol. 15, No. 3: pp. 1034-1080

Abstract

Let S$S$ be a surface of negative Euler characteristic and consider a finite filling collection Gamma$\Gamma$ of closed curves on S$S$ in minimal position. An observation of Foulon and Hasselblatt shows that PT(S) set minus Gamma$PT(S) \setminus \widehat {\Gamma }$ is a finite-volume hyperbolic 3-manifold, where PT(S)$PT(S)$ is the projectivized tangent bundle and Gamma$\widehat \Gamma$ is the set of tangent lines to Gamma$\Gamma$. In particular, vol(PT(S) set minus Gamma)$vol(PT(S) \setminus \widehat {\Gamma })$ is a mapping class group invariant of the collection Gamma$\Gamma$. When Gamma$\Gamma$ is a filling pair of simple closed curves, we show that this volume is coarsely comparable to Weil-Petersson distance between strata in Teichmuller space. Our main tool is the study of stratified hyperbolic links Gamma over bar $\overline{\Gamma }$ in a Seifert-fibered space N$N$ over S$S$. For such links, the volume of N set minus Gamma over bar $N\setminus \overline{\Gamma }$ is coarsely comparable to expressions involving distances in the pants graph.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Computer Science
• Subjects: 000 Computer science, information and general works > 004 Data processing computer science
• ISSN: 1753-8416
• Language: English