Algebraic string operations

Abstract

We first discuss how open/closed chord diagrams, both with and without marked points, act on appropriate Hochschild complexes possibly coupled with the two-sided cobar complex.Then, in the main part of the paper, we introduce the notion of a V kalgebra and obtain suitable homotopy versions.Contents 1. Introduction 1 2. Actions of chord diagrams for strict algebras 3 3. V ∞ -algebras 8 4. DG • ∞ and string operations 14 5.Some variations 23 References 31