Non-formality of Voronov's Swiss-Cheese operads
Abstract
The Swiss-Cheese operads, which encode actions of algebras over the little $n$-cubes operad on algebras over the little $(n-1)$-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 $(2, 2^n)$, rather than $(2, 0)$ (Livernet) or $(4, 0)$ (Willwacher).
Domains
Algebraic Topology [math.AT]
Fichier principal
2303.16979.pdf (2.81 Mo)
Télécharger le fichier
SwissCheeseCode.m (17.17 Ko)
Télécharger le fichier
SwissCheeseDemo.pdf (1.56 Mo)
Télécharger le fichier
Origin : Files produced by the author(s)
Licence : Copyright
Licence : Copyright
Licence : Public Domain
Licence : Copyright