Graph homology and graph configuration spaces

Abstract

If $R$ is a commutative ring, $M$ a compact $R$-oriented manifold and $G$ a finite graph without loops or multiple edges, we consider the graph configuration space $M^G$ and a Bendersky-Gitler type spectral sequence converging to the homology $H_{\ast }(M^G,R)$. We show that its $E_1$ term is given by the graph cohomology complex $C_A(G)$ of the graded commutative algebra $A=H^{\ast }(M,R)$ and its higher differentials are obtained from the Massey products of $A$, as conjectured by Bendersky and Gitler for the case of a complete graph $G$. Similar results apply to the spectral sequence constructed from an arbitrary finite graph $G$ and a graded commutative DG algebra $\mathcal{A}$.

15 pages, 2 figures

References in corpus (1)

• Transferring homotopy commutative algebraic structures