10.3336/gm Glasnik matematički ISSN 0017-095X (Tisak) ISSN 1846-7989 (Online) Hrvatsko matematičko društvo i PMF-Matematički odsjek Sveučilišta u Zagrebu Bijenička cesta 30, 10000 Zagreb glasnik@math.hr http://web.math.hr/glasnik/ 10.3336/gm.58.1.09 Izvorni znanstveni članak Big flip graphs and their automorphism groups Bar-Natan Assaf assafbarnatan@gmail.com 1 Goel Advay advayg@mit.edu 2 Halstead Brendan brendanhalstead23@gmail.com 3 Hamrick Paul hamri@unc.ed 4 Shenoy Sumedh sshenoy@mit.edu 5 Verma Rishi verma.rishiraj@gmail.com 6 Department of Mathematics, Brandeis University, 415 South Street, Waltham, MA 02453, USA Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA 02139, USA nbsp; UNC Chapel Hill Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA 02139, USA Stanford University 30 6 2023 Vol 58 Svezak 1 125 134

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.

 Flip graphs, infinite-type surfaces, mapping class groups, Ivanov