2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/157090We construct a geometric model for the mapping class group M of a non-exceptional oriented surface of finite type and use it to show that the action of M on the compact Hausdorff space of complete geodesic laminations is topologically amenable. As a consequence, the Novikov higher signature conjecture holds for every subgroup of M.59 pages. Section 5 simplified and corrected. Writing improved. Details addedGroup TheoryGeometric Topology20M34text