Automorphisms of the loop and arc graph of an infinite-type surface
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- by Anschel Schaffer-Cohen HTML | PDF
- Proc. Amer. Math. Soc. Ser. B 9 (2022), 230-240
Abstract:
We show that the extended based mapping class group of an infinite-type surface is naturally isomorphic to the automorphism group of the loop graph of that surface. Additionally, we show that the extended mapping class group stabilizing a finite set of punctures is isomorphic to the arc graph relative to that finite set of punctures. This extends a known result for sufficiently complex finite-type surfaces, and provides a new angle from which to study the mapping class groups of infinite-type surfaces.References
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Additional Information
- Anschel Schaffer-Cohen
- Affiliation: Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104
- MR Author ID: 1303454
- ORCID: 0000-0003-4885-258X
- Email: anschel@math.upenn.edu
- Received by editor(s): December 17, 2019
- Received by editor(s) in revised form: February 16, 2021
- Published electronically: April 29, 2022
- Communicated by: Kenneth Bromberg
- © Copyright 2022 by the author under Creative Commons Attribution-NonCommercial 3.0 License (CC BY NC 3.0)
- Journal: Proc. Amer. Math. Soc. Ser. B 9 (2022), 230-240
- MSC (2020): Primary 57K20, 20F65; Secondary 05C25
- DOI: https://doi.org/10.1090/bproc/83
- MathSciNet review: 4414904
Dedicated: For Carlos