Homotopy Gerstenhaber algebras are strongly homotopy commutative. Franz, M. arXiv:1907.04778 [math], July, 2019. arXiv: 1907.04778
Homotopy Gerstenhaber algebras are strongly homotopy commutative [link]Paper  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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