Non-formality of Voronov's Swiss-Cheese operads

Author(s)
Najib Idrissi, Renato Vasconcellos Vieira.
Publication
To appear in Q. J. Math.
Online on
Updated on
Accepted on
Full text
https://cdn.idrissi.eu/main/research/non-formality-swiss.pdf
DOI:10.1093/qmath/haad041
https://doi.org/10.1093/qmath/haad041
arXiv:2303.16979
https://arxiv.org/abs/2303.16979
hal-04053257
https://hal.science/hal-04053257
Annex code
https://github.com/nidrissi/non-formality-swiss-annex

Abstract

The Swiss-Cheese operads, which encode actions of algebras over the little nn-cubes operad on algebras over the little (n1)(n−1)-cubes operad, comes in several variants. We prove that the variant in which open operations must have at least one open input is not formal in characteristic zero. This is slightly stronger than earlier results of Livernet and Willwacher. The obstruction to formality that we find lies in arity (2,2n)(2,2^n), rather than (2,0)(2,0) (Livernet) or (4,0)(4,0) (Willwacher).