# Resolutions of strong homotopy Lie algebras

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Niek de Kleijn

created by lapastina on 11 Oct 2018

modified on 07 Jan 2019

25 oct 2018
-- 10:00

Sala Riunioni DipMat, Salerno

**Abstract.**

Given a smooth manifold M it turns out that a lot properties may be encoded in terms of the differential graded Lie algebra structure of the (smooth) Hochschild cochain complex of the algebra of smooth functions on M, i.e. in the space of polydifferential operators. In fact this complex can be adapted in various ways including importantly an adaptation to Lie algebroids (this generalizes or restricts the available notions of differential operators). One major tool in the use of the complex of polydifferential operators is the fact that it is formal, i.e. it is quasi-isomorphic as a strong homotopy Lie algebra to its cohomology differential graded Lie algebra. In this talk I will outline a reconceptualization of various methods used to prove this formality using the local formality as input. This is done by introducing the notion of resolution of strong homotopy Lie algebras.