The purpose of this work is to represent homotopy classes of maps from a surface $M$ to $S^2\vee S^1$ by maps with some minimal root properties.
"Representing homotopy classes by maps with certain minimality root properties II." Topol. Methods Nonlinear Anal. 56 (2) 473 - 482, 2020. https://doi.org/10.12775/TMNA.2020.056