Abstract
The framed n-discs operad fD_n 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 fD_n is equivalent to the n-fold loop space on a SO(n)-space. Examples of fD_2-spaces are nerves of ribbon braided monoidal categories. We compute the rational homology of fD_n. Koszul duality for semidirect product operads of chain complexes is defined and applied to compute the double loop space homology as BV-algebra.
| Original language | English |
|---|---|
| Journal | Quarterly Journal of Mathematics |
| Volume | 54 |
| Pages (from-to) | 213-231 |
| ISSN | 0033-5606 |
| Publication status | Published - 2003 |