Resumen de Weight 2 cohomology of graph complexes of cyclic operads and the handlebody group

Michael Borinsky, Benjamin Brück, Thomas Willwacher

• We compute the weight 2 cohomology of the Feynman transforms of the cyclic (co)operads BV and HyCom, and the top−2 weight cohomology of the Feynman transforms of DBV and Grav. Using a result of Giansiracusa, we compute, in particular, the top−2 weight cohomology of the handlebody group. We compare the result to the top−2 weight cohomology of the moduli space of curves Mg,n, recently computed by Payne and the last-named author. We also provide another proof of a recent result of Hainaut–Petersen identifying the top weight cohomology of the handlebody group with the Kontsevich graph cohomology.