2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64705We 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.This is the final version. The published version, which is slightly different, is available at http://nyjm.albany.edu:8000/PacJ/2003/v209-2.htmQuantum AlgebraGeometric Topology17B62,17B63,17B70,20F28,57M07,57M15,57M27text