We analyze a functor from
cyclic operads to chain complexes first considered by Getzler and Kapranov
and also by 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∞ and
co-Lie∞ structures. In particular, the chain complexes have a bracket and
cobracket which are compatible in the Lie bialgebra sense on a certain natural
subcomplex.
