Abstract
The nonorientable –genus of a knot is the smallest first Betti number of any nonorientable surface properly embedded in the –ball and bounding the knot . We study a conjecture proposed by Batson about the value of for torus knots, which can be seen as a nonorientable analogue of Milnor’s conjecture for the orientable –genus of torus knots. We prove the conjecture for many infinite families of torus knots, by calculating for all torus knots a lower bound for formulated by Ozsváth, Stipsicz and Szabó.
Citation
Stanislav Jabuka. Cornelia A Van Cott. "On a nonorientable analogue of the Milnor conjecture." Algebr. Geom. Topol. 21 (5) 2571 - 2625, 2021. https://doi.org/10.2140/agt.2021.21.2571
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