Curved infinity-algebras and their characteristic classes

Abstract

In this paper we study a natural extension of Kontsevich's characteristic class construction for A-infinity and L-infinity algebras to the case of curved algebras. These define homology classes on a variant of his graph homology which allows vertices of valence >0. We compute this graph homology, which is governed by star-shaped graphs with odd-valence vertices. We also classify nontrivially curved cyclic A-infinity and L-infinity algebras over a field up to gauge equivalence, and show that these are essentially reduced to algebras of dimension at most two with only even-ary operations. We apply the reasoning to compute stability maps for the homology of Lie algebras of formal vector fields. Finally, we explain a generalization of these results to other types of algebras, using the language of operads.

Final version, to appear in J. Topology. 28 pages

References in corpus (7)

• Nonhomogeneous quadratic duality and curvature
• Homotopy Batalin-Vilkovisky algebras
• Koszul duality for Operads
• Classes on compactifications of the moduli space of curves through solutions to the quantum master equation
• Dual Feynman transform for modular operads
• On the (non)vanishing of some "derived" categories of curved dg algebras
• Open-closed moduli spaces and related algebraic structures

Cited by in corpus (2)

• Formality conjecture for minimal surfaces of Kodaira dimension 0
• Formal Global AKSZ Gauge Observables and Generalized Wilson Surfaces