2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/112965We first discuss how open/closed chord diagrams, both with and without marked points, act on appropriate Hochschild complexes possibly coupled with the two-sided cobar complex. Then, in the main part of the paper, we introduce the notion of a V_k-algebra and obtain suitable homotopy versions.32 pages, 35 figuresQuantum AlgebraAlgebraic Topology16E40, 55U99text