Some properties of “bulky” links generated by generalized Möbius-Listing bodies \(\mathrm{GML}_4^n\). (English. Russian original) Zbl 1347.57008
J. Math. Sci., New York 216, No. 4, 509-518 (2016); translation from Sovrem. Mat. Prilozh. 94 (2014).
Summary: In the present paper, we consider the “bulky knots” and “bulky links” that appear after cutting of generalized Möbius-Listing \(\mathrm{GML}_4^n\) bodies (with corresponding radial cross sections square) along different generalized Möbius-Listing surfaces \(\mathrm{GML}_2^n\) situated in it. The aim of this article is to examine the number and geometric structure of independent objects that appear after such a cutting process of \(\mathrm{GML}_4^n\) bodies. In most cases, we are able to count the indices of the resulting mathematical objects according to the known tabulation for knots and links of small complexity.
MSC:
| 57M25 | Knots and links in the \(3\)-sphere (MSC2010) |
| 53A05 | Surfaces in Euclidean and related spaces |
| 68U05 | Computer graphics; computational geometry (digital and algorithmic aspects) |
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