2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/124401We show that the Kontsevich operad, as an operad with multiplication, provides a model for the Taylor tower of the functor defined by taking the homotopy fiber of the inclusion of embeddings of an interval in a cube to the corresponding space of immersions. In developing the Kontsevich operad, we find an operad structure on the simplicial model for the two-sphere, in the opposite category to finite sets. Applications of our result include using machinery of McClure-Smith to produce a little two-disk action on our knot spaces.v3. Final (published) version, incorporating referee comments. Binomial operad has been renamed choose-two operadAlgebraic TopologyQuantum Algebra57Q35; 57M25; 18D50text