Reference : Wheeled PROPs, graph complexes and the master equation
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Wheeled PROPs, graph complexes and the master equation
Markl, Martin [Czech Academy of Sciences > Mathematics > professor]
Merkulov, Sergei mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Shadrin, Sergei [University of Amsterdam > Mathematics > Professor]
Journal of Pure and Applied Algebra
Yes (verified by ORBilu)
[en] operads ; props ; quantization
[en] 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 of classical operads Com and Ass as non-trivial extensions of the well-known dg operads Com-infinityand Ass-infinity source. Finally, we apply the above results to a computation of cohomology of a directed version of Kontsevich’s complex of ribbon graphs.
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