The nonorientable –genus of a knot in the –sphere is defined as the smallest first Betti number of any nonorientable surface smoothly and properly embedded in the –ball with boundary the given knot. We compute the nonorientable –genus for all knots with crossing number or . As applications we prove a conjecture of Murakami and Yasuhara and compute the clasp and slicing number of a knot.
"The nonorientable $4$–genus for knots with $8$ or $9$ crossings." Algebr. Geom. Topol. 18 (3) 1823 - 1856, 2018. https://doi.org/10.2140/agt.2018.18.1823