2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/172814The group SL(n,Z) admits a smooth faithful action on the (n-1)-sphere S^(n-1), induced from its linear action on euclidean space R^n. We show that, if m < n-1 and n > 2, any smooth action of SL(n,Z) on a mod 2 homology m-sphere, and in particular on the m-sphere S^m, is trivial.5 pages; this is a corrected version which will appear in Top. Appl. 2008Geometric Topology57S25text