A bordism approach to string topology

Abstract

Using intersection theory in the context of Hilbert manifolds and geometric homology we show how to recover the main operations of string topology built by M. Chas and D. Sullivan. We also study and build an action of the homology of reduced Sullivan's chord diagrams on the singular homology of free loop spaces, extending previous results of R. Cohen and V. Godin and unifying part of the rich algebraic structure of string topology as an algebra over the prop of these reduced diagrams. Some of these operations are extended to spaces of maps from a sphere to a compact manifold.

Cited by in corpus (7)

• Infinity Properads and Infinity Wheeled Properads
• Notes on string topology
• The homotopy invariance of the string topology loop product and string bracket
• Higher string topology on general spaces
• Higher operations in string topology of classifying spaces
• Spectral Sequences in String Topology
• The loop-coproduct spectral sequence