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We make calculations in graph homology which further understanding of thetopology of spaces of string links, in particular calculating the Eulercharacteristics of finite-dimensional summands in their homology and homotopy.In doing so, we also determine the supercharacter of the symmetric group actionon the positive arity components of the modular envelope of $L_\infty$.

Euler characteristics for spaces of string links and the modular envelope of $L_\infty$