We prove a rigidity theorem for degree one maps between small 3–manifolds using Heegaard genus, and provide some applications and connections to Heegaard genus and Dehn surgery problems.
"Degree one maps between small 3–manifolds and Heegaard genus." Algebr. Geom. Topol. 5 (4) 1433 - 1450, 2005. https://doi.org/10.2140/agt.2005.5.1433