2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/135153In this note, we define the notion of a cactus set, and show that its geometric realization is naturally an algebra over Voronov's cactus operad, which is equivalent to the framed 2-dimensional little disks operad $\mathcal{D}_2$. Using this, we show that the Hochschild cohomology of a Poincaré algebra A is an algebra over (the chain complexes of) $\mathcal{D}_2$.12 pagesAlgebraic Topology55P48 (primary), 16E40 (secondary)text