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2018 The nonorientable $4$–genus for knots with $8$ or $9$ crossings
Stanislav Jabuka, Tynan Kelly
Algebr. Geom. Topol. 18(3): 1823-1856 (2018). DOI: 10.2140/agt.2018.18.1823

Abstract

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.

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Stanislav Jabuka. Tynan Kelly. "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

Information

Received: 29 August 2017; Revised: 30 November 2017; Accepted: 24 December 2017; Published: 2018
First available in Project Euclid: 26 April 2018

zbMATH: 06866414
MathSciNet: MR3784020
Digital Object Identifier: 10.2140/agt.2018.18.1823

Subjects:
Primary: 57M25, 57M27

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.18 • No. 3 • 2018
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