Summary
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 [14]. These results are based on the useful notion of a \(\frac{1}{2}\)PROP introduced by Kontsevich in [9].
2000 Mathematics Subject Classifications: 18D50, 55P48
Partially supported by the grant GA ÄŚR 201/02/1390 and by the Academy of Sciences of the Czech Republic, Institutional Research Plan No. AV0Z10190503.
Partially supported by NSF grant DMS-0227974.
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Dedicated to Yuri I. Manin on the occasion of his seventieth birthday
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Markl, M., Voronov, A.A. (2009). PROPped-Up Graph Cohomology. In: Tschinkel, Y., Zarhin, Y. (eds) Algebra, Arithmetic, and Geometry. Progress in Mathematics, vol 270. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4747-6_8
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DOI: https://doi.org/10.1007/978-0-8176-4747-6_8
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