The Non-Orientable 4-Genus of 11 Crossing Non-Alternating Knots

2024/03/01 by Megan Fairchild, Fairchild, Megan · 2 citations
Computer Science · Engineering · Mathematics · #Algebraic Topology (math.AT) #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Mathematics and Applications #Robotic Mechanisms and Dynamics

paper · pdf · doi:10.48550/arxiv.2403.00996

openalex publication_date 2024/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The non-orientable 4-genus of a knot K in the three sphere is defined to be the minimum first Betti number of a non-orientable surface F in the four-ball so that K bounds F. We will survey the tools used to compute the non-orientable 4-genus, and use various techniques to calculate this invariant for non-alternating 11 crossing knots. We also will view obstructions to a knot bounding a Möbius band given by the double branched cover of the three sphere branched over K.

Cited by

• An Algorithmic Search for Knots Bounding Möbius Bands in B⁴
• The Non-Orientable Four-Ball Genus of a New Infinite Family of Torus Knots

Related

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• Nonorientable surfaces bounded by knots: a geography problem
• An Algorithmic Search for Knots Bounding Möbius Bands in B⁴