Higher string topology operations

Abstract

Chas and Sullivan have defined an intersection-type product on the homology of the free loop space LM of an oriented manifold M. In this paper we show how to extend this construction to a topological conformal field theory of degree d. In particular, we get operations on the homology of LM which are parameterized by the homology of the moduli space of open-closed Riemann surfaces.

78 pages, 12 figures. Typos corrected, some proofs clarified

References in corpus (2)

• A polarized view of string topology
• The differential topology of loop spaces

Cited by in corpus (6)

• String Topology: Background and Present State
• Stable string operations are trivial
• Closed String TCFT for Hermitian Calabi-Yau Elliptic Spaces
• TQFT string operations in open-closed string topology
• Loop coproducts in string topology and triviality of higher genus TQFT operations
• Open-Closed TQFT String Operations for Disc Cobordisms, Simultaneous Saddle Interactions, and Constant Homology Classes