2002/08/31 by James Conant
Mathematics · #math.QA #math.GT #msc:17B62 #msc:17B63 #msc:17B70 #msc:20F28 #msc:57M07 #msc:57M15 #msc:57M27
published as Pac. J. Math, Vol. 209, No. 2, (2003) 219-230 · This is the final version. The published version, which is slightly different, is available at http://nyjm.albany.edu:8000/PacJ/2003/v209-2.htm
arxiv created 2003/08/08 · arxiv updated 2009/11/30
We analyze a functor from cyclic operads to chain complexes first considered by Getzler and Kapranov and also Markl. This functor is a generalization of the graph homology considered by Kontsevich, which was defined for the three operads Comm, Assoc, and Lie. More specifically we show that these chain complexes have a rich algebraic structure in the form of families of operations defined by fusion and fission. These operations fit together to form uncountably many Lie-infinity and co-Lie-infinity structures. In particular, the chain complexes have a bracket and cobracket which are compatible in the Lie bialgebra sense on a certain natural subcomplex.