2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/99973The goal of these notes is to prove that the mapping class groups of a closed orientable surface of genus two, with punctures, are not Kähler7 pages, no figures. v2: corrected typos and clarified some arguments. To be published in Proc. AMSAlgebraic GeometryGeometric Topologytext