On the homology of the double cobar construction of a double suspension

Alexandre Quesney (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

The double cobar construction of a double suspension comes with a Connes-Moscovici structure, that is a homotopy G-algebra (or Gerstenhaber-Voronov algebra) structure together with a particular BV-operator up to a homotopy. We show that the homology of the double cobar construction of a double suspension is a free BV-algebra. In characteristic two, a similar result holds for the underlying $2$-restricted Gerstenhaber algebra. These facts rely on a formality theorem for the double cobar construction of a double suspension.

Domaines: Topologie algébrique [math.AT]

Alexandre Quesney. On the homology of the double cobar construction of a double suspension. 2014. ⟨hal-01010468⟩