Graphs of curves for surfaces with finite-invariance index \(1\)

Lanier, Justin; Loving, Marissa

doi:10.3336/gm.57.1.08

Glasnik matematički, Vol. 57 No. 1, 2022.

Original scientific paper

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

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page 119-128

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APA 6th Edition

Lanier, J. & Loving, M. (2022). Graphs of curves for surfaces with finite-invariance index \(1\). Glasnik matematički, 57 (1), 119-128. https://doi.org/10.3336/gm.57.1.08

MLA 8th Edition

Lanier, Justin and Marissa Loving. "Graphs of curves for surfaces with finite-invariance index \(1\)." Glasnik matematički, vol. 57, no. 1, 2022, pp. 119-128. https://doi.org/10.3336/gm.57.1.08. Accessed 6 May 2024.

Chicago 17th Edition

Lanier, Justin and Marissa Loving. "Graphs of curves for surfaces with finite-invariance index \(1\)." Glasnik matematički 57, no. 1 (2022): 119-128. https://doi.org/10.3336/gm.57.1.08

Harvard

Lanier, J., and Loving, M. (2022). 'Graphs of curves for surfaces with finite-invariance index \(1\)', Glasnik matematički, 57(1), pp. 119-128. https://doi.org/10.3336/gm.57.1.08

Vancouver

Lanier J, Loving M. Graphs of curves for surfaces with finite-invariance index \(1\). Glasnik matematički [Internet]. 2022 [cited 2024 May 06];57(1):119-128. https://doi.org/10.3336/gm.57.1.08

IEEE

J. Lanier and M. Loving, "Graphs of curves for surfaces with finite-invariance index \(1\)", Glasnik matematički, vol.57, no. 1, pp. 119-128, 2022. [Online]. https://doi.org/10.3336/gm.57.1.08

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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.