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Open-closed field theories, string topology, and Hochschild homology
[unknown]

2009
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Contemporary Mathematics
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unpublished

In this expository paper we discuss a project regarding the string topology of a manifold, that was inspired by recent work of Moore-Segal [28] and Costello [17] on "open-closed topological conformal field theories". In particular, given a closed, oriented manifold M , we describe the "string topology category" SM , which is enriched over chain complexes over a fixed field k. The objects of SM are closed, oriented submanifolds N of M , and the space of morphisms between N1 and N2 is a chain

doi:10.1090/conm/504/09875
fatcat:wjjzuza7izg7xco2vcmxqsn5le