Ivanov's metaconjecture on automorphisms of rich surface objects

Let $S$ be a surface, and let an object be naturally associated to $S$ and have sufficiently rich structure. Ivanov's metaconjecture. Every such object has the extended mapping class group ${\operatorname{Map}^\pm}(S)$ as its group of automorphisms. This metaconjecture describes a pattern in which sufficiently rich objects associated to finite-type surfaces are characterized by the action of the extended mapping class group; the paper explains that it does not extend to simultaneous flip graphs of infinite-type surfaces.