Abstract
If R is a commutative ring, M a compact R-oriented manifold and G a finite graph without loops or multiple edges, we consider the graph configuration space M G and a Bendersky–Gitler type spectral sequence converging to the homology H *(M G, R). We show that its E 1 term is given by the graph cohomology complex C A (G) of the graded commutative algebra A = H*(M, R) and its higher differentials are obtained from the Massey products of A, as conjectured by Bendersky and Gitler for the case of a complete graph G. Similar results apply to the spectral sequence constructed from an arbitrary finite graph G and a graded commutative DG algebra \({\mathcal{A}}\).
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Communicated by Jim Stasheff.
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Baranovsky, V., Sazdanovic, R. Graph homology and graph configuration spaces. J. Homotopy Relat. Struct. 7, 223–235 (2012). https://doi.org/10.1007/s40062-012-0006-3
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DOI: https://doi.org/10.1007/s40062-012-0006-3