Properadic homotopical calculus

Eric Hoffbeck (1) , Johan Leray (2) , Bruno Vallette (3)

1 LAGA - Laboratoire Analyse, Géométrie et Applications
2 LAREMA - Laboratoire Angevin de Recherche en Mathématiques
3 LAGA - Laboratoire Analyse, Géométrie et Applications

In this paper, we initiate the generalisation of the operadic calculus which governs the properties of homotopy algebras to a properadic calculus which governs the properties of homotopy gebras over a properad. In this first article of a series, we generalise the seminal notion of infini-morphisms and the ubiquitous homotopy transfer theorem. As an application, we recover the homotopy properties of involutive Lie bialgebras developed by Cieliebak--Fukaya--Latschev and we produce new explicit formulas.

Domaines: Mathématiques [math]; Catégories et ensembles [math.CT]; Algèbres quantiques [math.QA]

Eric Hoffbeck, Johan Leray, Bruno Vallette. Properadic homotopical calculus. International Mathematics Research Notices, 2021, 2021 (5), pp.3866-3926. ⟨10.1093/imrn/rnaa091⟩. ⟨hal-02378816⟩