Glasnik Matematicki, Vol. 57, No. 1 (2022), 119-128. \( \)

GRAPHS OF CURVES FOR SURFACES WITH FINITE-INVARIANCE INDEX \(1\)

Justin Lanier and Marissa Loving

Department of Mathematics, University of Chicago, 5734 S. University Ave., Chicago, IL 60637, USA
e-mail:jlanier@math.uchicago.edu

Department of Mathematics, University of Wisconsin – Madison, 480 Lincoln Dr, Madison, WI 53706, USA
e-mail:mloving2@wisc.edu

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.

2020 Mathematics Subject Classification.   57K20, 57M15, 37E30

Key words and phrases.   Infinite-type surfaces, curve graphs, big mapping class groups.

Full text (PDF) (access from subscribing institutions only)

https://doi.org/10.3336/gm.57.1.08

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