2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/225612A necessary and sufficient algebraic condition for a diffeomorphism over a surface embedded in the 3-sphere to be induced by a regular homotopic deformation is discussed, and a formula for the number of signed pass moves needed for this regular homotopy is given.7 pages, 5 figuresGeometric Topology57M60; 57N10Regular homotopic deformation of compact surface with boundary and mapping class grouptext