Author:
Lanier Justin, ,Loving Marissa,
Abstract
In this note we make progress toward a conjecture of Durham–Fanoni–Vlamis, showing that every infinite-type surface with finite-invariance index \(1\) and no nondisplaceable compact subsurfaces fails to have a good graph of curves, that is, a connected graph where vertices represent homotopy classes of essential simple closed curves and with a natural mapping class group action having infinite diameter orbits. Our arguments use tools developed by Mann–Rafi in their study of the coarse geometry of big mapping class groups.
Publisher
University of Zagreb, Faculty of Science, Department of Mathematics
Reference13 articles.
1. J. Aramayona, private communication, 2018.
2. J. Aramayona and F. Valdez, On the geometry of graphs associated to infinite-type surfaces, Math. Z. 289 (2018), 309-322.
3. J. Aramayona and N. G. Vlamis, Big mapping class groups: an overview, arXiv:2003.07950, 2020.
4. J. Bavard, Hyperbolicité du graphe des rayons et quasi-morphismes sur un gros groupe modulaire, Geom. Topol., 20 (2016), 491-535.
5. D. Calegari, Big mapping class groups and dynamics, Geometry and the imagination, 2009.
Cited by
2 articles.
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