Glasnik Matematicki, Vol. 58, No. 1 (2023), 125-134. \( \)

BIG FLIP GRAPHS AND THEIR AUTOMORPHISM GROUPS

Assaf Bar-Natan, Advay Goel, Brendan Halstead, Paul Hamrick, Sumedh Shenoy and Rishi Verma

Department of Mathematics, Brandeis University, 415 South Street, Waltham, MA 02453, USA
e-mail:assafbarnatan@gmail.com

Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA 02139, USA
e-mail:advayg@mit.edu


e-mail:brendanhalstead23@gmail.com

UNC Chapel Hill
e-mail:hamri@unc.edu

Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA 02139, USA
e-mail:sshenoy@mit.edu

Stanford University
e-mail:verma.rishiraj@gmail.com

Abstract.   In this paper, we study the relationship between the mapping class group of an infinite-type surface and the simultaneous flip graph, a variant of the flip graph for infinite-type surfaces defined by Fossas and Parlier [6]. We show that the extended mapping class group is isomorphic to a proper subgroup of the automorphism group of the flip graph, unlike in the finite-type case. This shows that Ivanov's metaconjecture, which states that any “sufficiently rich" object associated to a finite-type surface has the extended mapping class group as its automorphism group, does not extend to simultaneous flip graphs of infinite-type surfaces.

2020 Mathematics Subject Classification.   57M60

Key words and phrases.   Flip graphs, infinite-type surfaces, mapping class groups, Ivanov

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

https://doi.org/10.3336/gm.58.1.09

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