Compactifying String Topology

Abstract

We study the string topology of a closed oriented Riemannian manifold M. We describe a compact moduli space of diagrams, and show how the cellular chain complex of this space gives algebraic operations on the singular chains of the free loop space LM of M. These operations are well-defined on the homology of a quotient of this moduli space, which has the homotopy type of a compactification of the moduli space of Riemann surfaces. In particular, our action of the 0-dimensional homology of the quotient space on the homology of the free loop space of M recovers the Cohen-Godin positive boundary TQFT.

55 pages, 7 figures

Cited by in corpus (8)

• Infinity Properads and Infinity Wheeled Properads
• On string topology of classifying spaces
• Chain-Level String Topology Operations
• Comparing fat graph models of moduli space
• Higher operations in string topology of classifying spaces
• The odd origin of Gerstenhaber brackets, Batalin-Vilkovisky operators, and master equations
• On Cohen-Jones isomorphism in string topology
• On the homotopy type of the space of Sullivan diagrams