
## 2. Big complexes

1. #### Problem 2.1.

[Katie Mann, Priyam Patel] What is the "right" combinatorial object to associate to a big mapping class group? Is there one complex that works for all surfaces, or is a patchwork approach more natural?
• #### Problem 2.2.

[Carolyn Abbott] For many big surfaces, we already have several complexes that are known to be hyperbolic. For these (and for others, as they’re added to the catalogue), what relationships exist between these graphs? For instance, for a given surface, are they quasi-isometric? Are there Lipschitz maps between them?
• #### Problem 2.3.

[Katie Mann] Classify big surfaces whose mapping class groups act by unbounded orbits on (hyperbolic) connected locally finite complexes.

Cite this as: AimPL: Surfaces of infinite type, available at http://aimpl.org/genusinfinity.