Swiss Cheese type operads and models for relative loop spaces

Alexandre Quesney (1)

1 UFPR - Universidade Federal do Parana [Curitiba]

We construct a (coloured) operad RL in the category of sets that may be thought of as a combinatorial model for the Swiss Cheese operad. By adapting Batanin-Berger's condensation process we obtain a topological (resp. chain) operad weakly equivalent to the topological (resp. chain) Swiss Cheese operad. As an application, we exhibit models for relative loop spaces acted on by Swiss Cheese type operads (in dimension 2).

Domaines: Topologie algébrique [math.AT]

Alexandre Quesney. Swiss Cheese type operads and models for relative loop spaces. 2015. ⟨hal-01227667v2⟩