Fusion and fission in graph complexes
Abstract
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.
Cite
@article{arxiv.math/0208093,
title = {Fusion and fission in graph complexes},
author = {James Conant},
journal= {arXiv preprint arXiv:math/0208093},
year = {2007}
}
Comments
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