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Algebra, Arithmetic, and Geometry pp 249–281Cite as

PROPped-Up Graph Cohomology

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Part of the book series: Progress in Mathematics ((PM,volume 270))

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 ČR 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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Author information

Authors and Affiliations

  1. Institute of Mathematics, Academy of Sciences, Žitná 25, 115 67, Praha 1, The Czech Republic

    M. Markl

  2. School of Mathematics, University of Minnesota, 206 Church St. S.E., Minneapolis, MN, 55455, USA

    A. A. Voronov

Authors
  1. M. Markl
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  2. A. A. Voronov
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Corresponding author

Correspondence to M. Markl .

Editor information

Editors and Affiliations

  1. Courant Inst. Mathematical, New York University, Mercer St. 251, New York, 10012, USA

    Yuri Tschinkel

  2. Eberly College of Science, Pennsylvania State University, University Park, 16802, USA

    Yuri Zarhin

Additional information

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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