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 (3)

• A polarized view of string topology
• The homotopy invariance of the string topology loop product and string bracket
• The differential topology of loop spaces

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