Algebraic String Operations

TL;DR

This paper explores algebraic string operations through the action of open/closed chord diagrams on Hochschild complexes and introduces V_k-algebras with their homotopy versions.

Contribution

It introduces the concept of V_k-algebras and develops their homotopy versions, expanding the algebraic framework for string operations.

Findings

Chord diagrams act on Hochschild complexes with marked points.

Introduction of V_k-algebras and their homotopy counterparts.

Establishment of a new algebraic structure for 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_k-algebra and obtain suitable homotopy versions.