2006/06/02 by Ralph M. Kaufmann, Kaufmann, Ralph M.
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #math.AG #math.AT #math.GT #math.QA #math.RA
paper · pdf · doi:10.48550/arxiv.math/0606065
50 pages, 8 figures. Newer version has minor changes. Some material is shifted. Typos and other small are things corrected
openalex publication_date 2006/06/02 · arxiv created 2006/10/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.