Automorphisms of the fine curve graph
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- by Adele Long, Dan Margalit, Anna Pham, Yvon Verberne and Claudia Yao;
- Trans. Amer. Math. Soc.
- DOI: https://doi.org/10.1090/tran/9374
- Published electronically: May 1, 2025
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Abstract:
Building on work of Farb and the second author, we prove that the group of automorphisms of the fine curve graph for a surface is isomorphic to the group of homeomorphisms of the surface. This theorem is analogous to the seminal result of Ivanov that the group of automorphisms of the (classical) curve graph is isomorphic to the extended mapping class group of the corresponding surface.References
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Bibliographic Information
- Adele Long
- Affiliation: Smith College, 1 Chapin Way, Unit 8281, Northampton, Massachusetts 01063
- MR Author ID: 1619040
- Email: AdeleLRLong@gmail.com
- Dan Margalit
- Affiliation: Vanderbilt University, Department of Mathematics, Nashville, Tennessee
- MR Author ID: 706322
- ORCID: 0000-0002-0370-3268
- Email: dan.margalit@vanderbilt.edu
- Anna Pham
- Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin
- MR Author ID: 1610639
- Email: tpham22@wisc.edu
- Yvon Verberne
- Affiliation: Western University, Department of Mathematics, Middlesex College, London, Ontario, Canada
- MR Author ID: 1162446
- Email: yverber@uwo.ca
- Claudia Yao
- Affiliation: Harvard University, Department of Mathematics, Cambridge, Massachusetts
- Email: wenxiyao@math.harvard.edu
- Received by editor(s): August 26, 2021
- Received by editor(s) in revised form: November 18, 2021, and December 9, 2021
- Published electronically: May 1, 2025
- Additional Notes: This material is based upon work supported by the National Science Foundation under Grant Nos. DMS-181843 and DMS-1811941. The fourth author is partially supported by an NSERC–PDF Fellowship.
- © Copyright 2025 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
- MSC (2020): Primary 57K20; Secondary 20F65, 57M07
- DOI: https://doi.org/10.1090/tran/9374