Homotopy Gerstenhaber algebras are strongly homotopy commutative
arXiv:1907.04778 · doi:10.1007/s40062-020-00268-y
Abstract
We show that any homotopy Gerstenhaber algebra is naturally a strongly homotopy commutative (shc) algebra in the sense of Stasheff-Halperin with a homotopy associative structure map. In the presence of certain additional operations corresponding to a cup-1 product on the bar construction, the structure map becomes homotopy commutative, so that one obtains an shc algebra in the sense of Munkholm.
33 pages; one reference added, minor changes