Discrete Representation of Cubical 2-Knots

Gabriela Hinojosa (), Ana Baray and Juan Pablo Díaz ()
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Gabriela Hinojosa: Universidad Autónoma del Estado de Morelos, Centro de Investigación en Ciencias
Ana Baray: Universidad Autónoma del Estado de Morelos, Centro de Investigación en Ciencias
Juan Pablo Díaz: Universidad Autónoma del Estado de Morelos, Centro de Investigación en Ciencias

A chapter in Handbook of Visual, Experimental and Computational Mathematics, 2026, pp 55-76 from Springer

Abstract: Abstract A cubical 2-knot K 2 ⊂ ℝ 4 $$K^2\subset \mathbb {R}^4$$ is an embedding of the 2-sphere in the 2-skeleton of the canonical cubulation of ℝ 4 $$\mathbb {R}^4$$ . In this paper, we describe cubical 2-knots in a discrete way, i.e., as a sequence of a finite number of points; in particular, we prove that there exists a generic projection p : ℝ 4 → P $$p:\mathbb {R}^4\rightarrow P$$ onto a suitable hyperplane P such that p ( K ) $$p(K)$$ is a knot diagram and using this fact, we develop an algorithm to compute its fundamental group.

Keywords: 2-Knots; Cubical knots; Honeycomb; Cubulated moves; Discrete knots; Fundamental group; Algorithms (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/978-3-032-16368-4_7

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