Ben Ward: Massey Products for graph homology

ABSTRACT: Graph complexes are combinatorial objects which can be used to compute invariants of topological spaces. This talk concerns the variant of graph complexes with ``hairs'' in which graphs may be disassembled into hopefully bite sized pieces by cutting apart the edges of a graph. This operation isn't necessarily well behaved when passing to homology, but it's failure to be well behaved can be encoded by a family of higher operations which we will introduce in the second half of this talk. The technical foundation of these results is the fact that the space of bracketings of a graph is always contractible. Part one of this talk will present a proof of this fact. In particular part one should (theoretically) be accessible to an undergraduate.