Parametrized L-infinity Spaces

2016/03/22 by Grady, Ryan E.
#Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1603.06930

Abstract

Motivated by families of formal moduli problems, in this note we generalize the notion of L-infinity space by allowing sheaves of L-infinity algebras over any (reasonable) nilpotent dg manifold. We discuss various examples including those coming from Lie algebroids. Given a Lie algebroid, we show that there is an L-infinity space parametrized by (cochains of) the Lie algebroid; further, characteristic classes of this L-infinity space recover the primary invariants of the original algebroid.

Related

• Maurer-Cartan spaces of filtered L-infinity algebras
• E-infinity structures over L-algebras
• L_infinity algebras as 1-jets of simplicial manifolds (and a bit beyond)
• Continuous and Twisted L_infinity Morphisms
• Models for classifying spaces and derived deformation theory