PROPped-up graph cohomology

M. Markl, A. A. Voronov

Research output: Chapter in Book/Report/Conference proceedingChapter

7 Scopus citations

Abstract

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 1/2 PROP introduced by Kontsevich in [9].

Original languageEnglish (US)
Title of host publicationProgress in Mathematics
PublisherSpringer Basel
Pages249-281
Number of pages33
DOIs
StatePublished - 2009

Publication series

NameProgress in Mathematics
Volume270
ISSN (Print)0743-1643
ISSN (Electronic)2296-505X

Bibliographical note

Funding Information:
∗Partially supported by the grant GA CˇR 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.

Funding Information:
Partially supported by the grant GA ?R 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.

Publisher Copyright:
© Springer Science+Business Media, LLC 2009.

Keywords

  • Cohomology
  • Graph complexes
  • Operads

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