Differentials on Graph Complexes III - Deleting a Vertex (1602.08316v3)

Abstract: We prove that the hairy graph complex with the extra differential is almost acyclic. This justifies the construction of hairy graph cohomology classes by the waterfall mechanism. The main idea used in the paper is a new differential, deleting a vertex. We hope that the new differential can have further applications in the study of graph cohomology.