Resumen de Filtrations on graph complexes and the Grothendieck–Teichmüller Lie algebra in depth two
Matteo Felder
We establish an isomorphism between the Grothendieck–Teichmüller Lie algebra grt1 in depth two modulo higher depth and the cohomology of the two-loop part of the graph complex of internally connected graphs ICG(1) . In particular, we recover all linear relations satisfied by the brackets of the conjectural generators σ2k+1 modulo depth three by considering relations among two-loop graphs. The Grothendieck–Teichmüller Lie algebra is related to the zeroth cohomology of Kontsevich’s graph complex GC2 via Willwacher’s isomorphism. We define a descending filtration on H0(GC2) and show that the degree two components of the corresponding associated graded vector spaces are isomorphic under Willwacher’s map.
