@article{c9271ed876324288a0e233b1e7e8ed24,
title = "On volumes and filling collections of multicurves",
abstract = "Let (Formula presented.) be a surface of negative Euler characteristic and consider a finite filling collection (Formula presented.) of closed curves on (Formula presented.) in minimal position. An observation of Foulon and Hasselblatt shows that (Formula presented.) is a finite-volume hyperbolic 3-manifold, where (Formula presented.) is the projectivized tangent bundle and (Formula presented.) is the set of tangent lines to (Formula presented.). In particular, (Formula presented.) is a mapping class group invariant of the collection (Formula presented.). When (Formula presented.) is a filling pair of simple closed curves, we show that this volume is coarsely comparable to Weil–Petersson distance between strata in Teichm{\"u}ller space. Our main tool is the study of stratified hyperbolic links (Formula presented.) in a Seifert-fibered space (Formula presented.) over (Formula presented.). For such links, the volume of (Formula presented.) is coarsely comparable to expressions involving distances in the pants graph.",
author = "Tommaso Cremaschi and Rodrigu{\'r}z-Migueles, {Jos{\'e} Andr{\'e}s} and Andrew Yarmola",
note = "Funding Information: The first and second author would like to thank Ian Biringer for inspiring conversations. The second author thanks Pekka Pankka for discussions on these topics. The second author gratefully acknowledges support from the Academy of Finland project 297258 {\textquoteleft}Topological Geometric Function Theory{\textquoteright} also from the grant 346300 for IMPAN from the Simons Foundation and the matching 2015‐2019 Polish MNiSW fund. The third author would like to thank David Gabai for helpful discussions and Princeton University for continued support. Funding Information: The first and second author would like to thank Ian Biringer for inspiring conversations. The second author thanks Pekka Pankka for discussions on these topics. The second author gratefully acknowledges support from the Academy of Finland project 297258 {\textquoteleft}Topological Geometric Function Theory{\textquoteright} also from the grant 346300 for IMPAN from the Simons Foundation and the matching 2015-2019 Polish MNiSW fund. The third author would like to thank David Gabai for helpful discussions and Princeton University for continued support. Publisher Copyright: {\textcopyright} 2022 The Authors. Journal of Topology is copyright {\textcopyright} London Mathematical Society.",
year = "2022",
month = sep,
doi = "10.1112/topo.12246",
language = "English (US)",
volume = "15",
pages = "1107--1153",
journal = "Journal of Topology",
issn = "1753-8416",
publisher = "John Wiley and Sons Ltd",
number = "3",
}