Publication date: 30 June 2022
Volume: Vol 57
Issue: Svezak 1
Pages: 119-128
DOI: https://doi.org/10.3336/gm.57.1.08
Izvorni znanstveni članak
https://doi.org/10.3336/gm.57.1.08
Graphs of curves for surfaces with finite-invariance index \(1\)
Justin Lanier
; Department of Mathematics, University of Chicago, 5734 S. University Ave., Chicago, IL 60637, USA
Marissa Loving
; Department of Mathematics, University of Wisconsin – Madison, 480 Lincoln Dr, Madison, WI 53706, USA
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.
Infinite-type surfaces, curve graphs, big mapping class groups.
279803
28.6.2022.
Posjeta: 325 *