Cubulated moves for 2-knots

2017/08/24 by Juan Pablo Díaz, Díaz, Juan Pablo, Gabriela Hinojosa +3 · 1 citation
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #math.GT

paper · pdf · doi:10.48550/arxiv.1708.07761

9 figures. arXiv admin note: text overlap with arXiv:1302.2133

arxiv created 2017/08/24 · arxiv updated 2017/08/28

Abstract

In this paper, we prove that given two cubical links of dimension two in \mathbb R⁴, they are isotopic if and only if one can pass from one to the other by a finite sequence of cubulated moves. These moves are analogous to the Reidemeister and Roseman moves for classical tame knots of dimension one and two, respectively.

Citations

• Cubulated moves and discrete knots

Cited by

• Minimal area of the spun trefoil knot on the canonical cubulation of ℝ⁴

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