The non-orientable 4-genus for knots with 8 or 9 crossings

Stanislav Jabuka; Tynan Kelly

doi:10.2140/agt.2018.18.1823

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arXiv · 1708.03000

The non-orientable 4-genus for knots with 8 or 9 crossings

Stanislav Jabuka·Tynan Kelly

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Abstract

The non-orientable 4-genus of a knot in the 3-sphere is defined as the smallest first Betti number of any non-orientable surface smoothly and properly embedded in the 4-ball, with boundary the given knot. We compute the non-orientable 4-genus for all knots with crossing number 8 or 9. As applications we prove a conjecture of Murakami's and Yasuhara's, and give a new lower bound for the slicing number of knot.

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BibTeX RIS

Stanislav Jabuka, Tynan Kelly. 2017-08-09. The non-orientable 4-genus for knots with 8 or 9 crossings. https://doi.org/10.2140/agt.2018.18.1823

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