## Framed discs operads and the equivariant recognition principle

by
Paolo Salvatore
,
Nathalie Wahl

Citations: | 8 - 0 self |

### BibTeX

@TECHREPORT{Salvatore_frameddiscs,

author = {Paolo Salvatore and Nathalie Wahl},

title = {Framed discs operads and the equivariant recognition principle},

institution = {},

year = {}

}

### OpenURL

### Abstract

The framed n-discs operad fDn is studied as semidirect product of SO(n) and the little n-discs operad. Our equivariant recognition principle says that a grouplike space acted on by fDn is equivalent to the n-fold loop space on a SO(n)-space. Examples of fD2-spaces are nerves of ribbon braided monoidal categories. We compute the rational homology of fDn. Koszul duality for semidirect product operads of chain complexes is defined and applied to compute the double loop space homology as BV-algebra. MSC(2000): 55P48, 18D10.