Implications of contractible or acyclic losing-coalition complexes
Establish what constraints or conclusions about a simple game can be derived when its simplicial complex of losing coalitions is contractible or when it is acyclic (has trivial homology).
References
If, say, the simplicial complex of losing coalitions is contractible, does that imply anything about the game? If the complex is acyclic, i.e. has trivial homology, what can we say about the game?
— The topology of simple games
(Volic et al., 16 Mar 2025) in Section 6 (Further work)