PROPped up graph cohomology

Details PROPped up graph cohomology PROPped up graph cohomology

2003-07-07

arxiv.org/abs/math/0307081v3

Mathematics

Quantum Algebra

33 pages; this is a final version to appear in Maninfest; some corrections made, including adding a condition of connectedness

Scientific paper

We consider graph complexes with a flow and compute their cohomology. More specifically, we prove that for a PROP generated by a Koszul dioperad, the corresponding graph complex gives a minimal model of the PROP. We also give another proof of the existence of a minimal model of the bialgebra PROP from math.AT/0209007. These results are based on the useful notion of a 1/2 PROP introduced by Kontsevich in an e-mail message to the first author.

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