Abstract
Let G be a topological group. Then the based loopspace of G is an algebra over the cacti operad, while the double loopspace of the classifying space of G is an algebra over the framed little discs operad. This paper shows that these two algebras are equivalent, in the sense that they are weakly equivalent E-algebras, where E is an operad weakly equivalent to both framed little discs and cacti. We recover the equivalence between cacti and framed little discs, and Menichi's isomorphism between the BV-algebras obtained by taking the homology of the loopspace of G and of the double loopspace of BG.
Original language | English |
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Pages (from-to) | 2597-2636 |
Number of pages | 40 |
Journal | Transactions of the American Mathematical Society |
Volume | 365 |
Issue number | 5 |
Early online date | 1 Oct 2012 |
DOIs | |
Publication status | Published - May 2013 |