Journal
JOURNAL OF PURE AND APPLIED ALGEBRA
Volume 213, Issue 4, Pages 496-535Publisher
ELSEVIER
DOI: 10.1016/j.jpaa.2008.08.007
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Funding
- European Commission through its 6th Framework Programme Structuring the European Research Area
- Academy of Sciences of the Czech Republic, Institutional Research Plan [AV0Z10190503]
- Goran Gustafsson foundation
- [Nr. RITA-CT-2004-505493]
- [GA CR 201/05/2117]
- [NWO-RFBR-047.011.2004.026 (RFBR-05-02-89000-NWO-a)]
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We introduce and study wheeled PROPs, an extension of the theory of PROPs which can treat traces and, in particular, solutions to the master equations which involve divergence operators. We construct a dg free wheeled PROP whose representations are in one-to-one correspondence with formal germs of SP-manifolds, key geometric objects in the theory of Batalin-Vilkovisky quantization. We also construct minimal wheeled resolutions If classical operads Corn and Ass as non-trivial extensions of the well-known dg operads Com(infinity) and Ass(infinity). Finally, we apply the above results to a computation of cohomology of a directed version of Kontsevich's complex of ribbon graphs. (C) 2008 Elsevier B.V. All rights reserved.
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