2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68012This paper concerns rigidity of the mapping class groups. We show that any homomorphism $ϕ:{\rm Mod}_g\to {\rm Mod}_h$ between mapping class groups of closed orientable surfaces with distinct genera $g>h$ is trivial if $g\geq 3$ and has finite image for all $g\geq 1$. Some implications are drawn for more general homomorphs of these groups.11 pages, 2 picturesGeometric TopologyGroup Theorytext