2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62650In this paper we study the topology of the strata, indexed by number partitions $λ$, in the natural stratification of the space of monic hyperbolic polynomials of degree $n$. We prove stabilization theorems for removing an independent block or an independent relation in $λ$. We also prove contractibility of the one-point compactifications of the strata indexed by a large class of number partitions, including $λ=(k^m,1^r)$, for $m\geq 2$. Furthermore, we study the maps between the homology groups of the strata, induced by imposing additional relations (resonances) on the number partition $λ$, or by merging some of the blocks of $λ$.CombinatoricsAlgebraic Topology32S20; 05E15, 32S60, 58K15text