The non-orientable 4-genus for knots with 10 crossings

2020/11/06 by Nakisa Ghanbarian, Ghanbarian, Nakisa · 3 citations
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2011.03480

openalex publication_date 2020/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a knot in the 3-sphere, the non-orientable 4-genus or 4-dimensional crosscap number of a knot is the minimal first Betti number of non-orientable surfaces, smoothly and properly embedded in the 4-ball, with boundary the knot. In this paper, we calculate the non-orientable 4-genus of knots with crossing number 10.

Cited by

• An Algorithmic Search for Knots Bounding Möbius Bands in B⁴
• Band-unknotting numbers and connected sums of knots
• The Non-Orientable Four-Ball Genus of a New Infinite Family of Torus Knots

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• Nonorientable four-ball genus can be arbitrarily large
• Non-orientable 4-genus of torus knots
• On a Refinement of the Non-Orientable 4-genus of Torus Knots
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