Top homology of hypergraph matching complexes, $p$-cycle complexes and Quillen complexes of symmetric groups

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/167552We investigate the representation of a symmetric group $S_n$ on the homology of its Quillen complex at a prime $p$. For homology groups in small codimension, we derive an explicit formula for this representation in terms of the representations of symmetric groups on homology groups of $p$-uniform hypergraph matching complexes. We conjecture an explicit formula for the representation of $S_n$ on the top homology group of the corresponding hypergraph matching complex when $n \equiv 1 \bmod p$. Our conjecture follows from work of Bouc when $p=2$, and we prove the conjecture when $p=3$.25 pagesGroup TheoryCombinatorics20D30; 05E25Top homology of hypergraph matching complexes, $p$-cycle complexes and Quillen complexes of symmetric groupstext