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Higher string topology operations
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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.
Forward citations
Cited by 3 Pith papers
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Smooth functions that split a Klein bottle into two M\"obius bands
The orbit component of a smooth function on a Klein bottle that splits into two Möbius bands is homotopy equivalent to the product of the orbit components of its restrictions to the two bands.
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Graded Frobenius Algebras
Graded Frobenius algebras are defined via a graph-based PROP, and an equivalence with explicit map-and-relation descriptions, including all required signs, is proved.
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