Geodesic
The nonorientable 4–genus for knots with 8 or 9 crossings
Jabuka, Stanislav1 ; Kelly, Tynan1
1 Department of Mathematics and Statistics, University of Nevada, Reno, NV, United States
Algebraic and Geometric Topology, Tome 18 (2018) no. 3, pp. 1823-1856

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The nonorientable 4–genus of a knot in the 3–sphere is defined as the smallest first Betti number of any nonorientable surface smoothly and properly embedded in the 4–ball with boundary the given knot. We compute the nonorientable 4–genus for all knots with crossing number 8 or 9. As applications we prove a conjecture of Murakami and Yasuhara and compute the clasp and slicing number of a  knot. An errata was submitted on 18 August 2020 and posted online on 1 December 2020.

DOI : 10.2140/agt.2018.18.1823
Classification : 57M25, 57M27
Keywords: knots, nonorientable 4-genus, crosscap number, slicing number

Jabuka, Stanislav 1 ; Kelly, Tynan 1

1 Department of Mathematics and Statistics, University of Nevada, Reno, NV, United States 
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Jabuka, Stanislav; Kelly, Tynan. The nonorientable 4–genus for knots with 8 or 9 crossings. Algebraic and Geometric Topology, Tome 18 (2018) no. 3, pp. 1823-1856. doi: 10.2140/agt.2018.18.1823

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