Moduli space actions on the Hochschild co-chains of a Frobenius algebra II: Correlators

Details Moduli space actions on the Hochschild co-chains of a Frobenius algebra II: Correlators Moduli space actions on the Hochschild co-chains of a Frobenius algebra II: Correlators

2006-06-02

arxiv.org/abs/math/0606065v2

Mathematics

Algebraic Topology

50 pages, 8 figures. Newer version has minor changes. Some material is shifted. Typos and other small are things corrected

Scientific paper

This is the second of two papers in which we prove that a cell model of the moduli space of curves with marked points and tangent vectors at the marked points acts on the Hochschild co--chains of a Frobenius algebra. We also prove that a there is dg--PROP action of a version of Sullivan Chord diagrams which acts on the normalized Hochschild co-chains of a Frobenius algebra. These actions lift to operadic correlation functions on the co--cycles. In particular, the PROP action gives an action on the homology of a loop space of a compact simply--connected manifold. In this second part, we discretize the operadic and PROPic structures of the first part. We also introduce the notion of operadic correlation functions and use them in conjunction with operadic maps from the cell level to the discretized objects to define the relevant actions.

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