Topological type of losing-coalition complexes and game structure
Determine how the topological type of the simplicial complex of losing coalitions (e.g., non-orientable spaces such as a Möbius strip or projective space versus orientable spaces such as a torus or sphere) influences or determines the structural properties of the associated simple game, and establish whether such games are structurally distinct across these topological types.
References
Along these lines, if the simplicial complex of losing coalitions has interesting topology in the sense that it is, for example, non-orientable and is perhaps homeomorphic to the Möbius strip or a projective space, what does that mean in terms of the game? Are games like that structurally different than those represented by, say, a torus or a sphere?
— The topology of simple games
(Volic et al., 16 Mar 2025) in Section 6 (Further work)