Swiss-cheese action on the totalization of operads under the monoid actions actions operad

Abstract

We prove that if a pair of semi-cosimplicial spaces (X,Y) arise from a coloured operad then the semi-totalization sTot(Y) has the homotopy type of a relative double loop space and the pair (sTot(X),sTot(Y)) is weakly equivalent to an explicit algebra over the two dimensional Swiss-cheese operad.

29 pages

References in corpus (2)

• Long knots and maps between operads
• On the rational homology of high dimensional analogues of spaces of long knots

Cited by in corpus (3)

• Relative Recognition Principle
• Formality of a higher-codimensional Swiss-Cheese operad
• Boardman-Vogt resolutions and bar/cobar constructions of (co)operadic (co)bimodules