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In this paper, we study the relationship between the mapping class group ofan infinite-type surface and the simultaneous flip graph, a variant of the flipgraph for infinite-type surfaces defined by Fossas and Parlier. We show thatthe extended mapping class group is isomorphic to a proper subgroup of theautomorphism group of the flip graph, unlike in the finite-type case. Thisshows that Ivanov's metaconjecture, which states that any "sufficiently rich"object associated to a finite-type surface has the extended mapping class groupas its automorphism group, does not extend to simultaneous flip graphs ofinfinite-type surfaces.

Big Flip Graphs and Their Automorphism Groups