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

Alexandre Quesney

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arXiv · 1406.5491

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

Alexandre Quesney

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Abstract

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.

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Alexandre Quesney. 2014-06-20. On the homology of the double cobar construction of a double suspension. https://arxiv.org/abs/1406.5491

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