Algebraic String Operations
Thomas Tradler, Mahmoud Zeinalian

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.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Combinatorial Mathematics
