Homotopy Gerstenhaber algebras are strongly homotopy commutative. Franz, M. *arXiv:1907.04778 [math]*, July, 2019. arXiv: 1907.04778Paper abstract bibtex We show that any homotopy Gerstenhaber algebra is canonically 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.

@article{franz_homotopy_2019,
title = {Homotopy {Gerstenhaber} algebras are strongly homotopy commutative},
url = {http://arxiv.org/abs/1907.04778},
abstract = {We show that any homotopy Gerstenhaber algebra is canonically 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.},
urldate = {2019-07-16},
journal = {arXiv:1907.04778 [math]},
author = {Franz, Matthias},
month = jul,
year = {2019},
note = {arXiv: 1907.04778},
keywords = {16E45 (Primary), 57T30 (Secondary), Mathematics - Algebraic Topology, mentions sympy},
}

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