Graph cohomologies and rational homotopy type of configuration spaces
We compare the cohomology complex defined by Baranovsky and Sazdanovi\'{c}, that is the $E_{1}$ page of a spectral sequence converging to the homology of the configuration space depending on a graph, with the rational model for the configuration space given by Kriz and Totaro. In particular we generalize the rational model to any graph and to an algebra over any field. We show that the dual of the Baranovsky and Sazdanovi\'{c}'s complex is quasi equivalent to this generalized version of the Kriz's model.
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Algebraic Topology
Category Theory
Rings and Algebras