Chain-Level String Topology Operations

Abstract

We construct a space of string diagrams, which are a type of fatgraph with some additional data, and show that there are string topology operations on the chains of the free loop space of a closed Riemannian manifold which are parameterized by the chains on the space of string diagrams. These operations are shown to recover known structure on homology of the free loop space.

67 pages, 23 figures

References in corpus (3)

• Riemannian Center of Mass and so called karcher mean
• A dual point of view on the ribbon graph decomposition of moduli space
• Compactifying String Topology

Cited by in corpus (5)

• Comparing fat graph models of moduli space
• Comparing combinatorial models of moduli space and their compactifications
• A chain level Batalin-Vilkovisky structure in string topology via de Rham chains
• On the homotopy type of the space of Sullivan diagrams
• On the invariance of the string topology coproduct