PROPped-up graph cohomology

M. Markl; A. A. Voronov

doi:10.1007/978-0-8176-4747-6_8

PROPped-up graph cohomology

M. Markl, A. A. Voronov

School of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

13 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 language	English (US)
Title of host publication	Progress in Mathematics
Publisher	Springer Basel
Pages	249-281
Number of pages	33
DOIs	https://doi.org/10.1007/978-0-8176-4747-6_8
State	Published - 2009

Publication series

Name	Progress in Mathematics
Volume	270
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

Publisher link

10.1007/978-0-8176-4747-6_8

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title = "PROPped-up graph cohomology",

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].",

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T1 - PROPped-up graph cohomology

AU - Markl, M.

AU - Voronov, A. A.

N1 - 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.

PY - 2009

Y1 - 2009

N2 - 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].

AB - 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].

KW - Cohomology

KW - Graph complexes

KW - Operads

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M3 - Chapter

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T3 - Progress in Mathematics

SP - 249

EP - 281

BT - Progress in Mathematics

PB - Springer Basel

ER -

PROPped-up graph cohomology

Abstract

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