We show that any graph product of finitely generated groups is hierarchically hyperbolic relative to its vertex groups. apply this result answer two questions Behrstock, Hagen, and Sisto: we the syllable metric on forms a space, products are themselves This last strengthening Berlai Robbio by removing need for extra hypotheses groups.We also Genevois about geometry electrification finite

Abstract This paper shows that the operad encoding modular operads is Koszul. Using this result, we construct higher composition operations on (hairy) graph homology, which characterize its rational homotopy type.