Link invariants derived from multiplexing of crossings
| Autor: | Haruko A. Miyazawa, Kodai Wada, Akira Yasuhara |
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| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
Link diagram 010102 general mathematics Diagram MathematicsofComputing_GENERAL Alexander polynomial Geometric Topology (math.GT) multiplexing of crossings 01 natural sciences Multiplexing welded link Mathematics - Geometric Topology 57M27 generalized link group 57M25 0103 physical sciences FOS: Mathematics Point (geometry) 010307 mathematical physics Geometry and Topology 0101 mathematics Virtual link Link (knot theory) Mathematics |
| Zdroj: | Algebr. Geom. Topol. 18, no. 4 (2018), 2497-2507 |
| DOI: | 10.48550/arxiv.1708.06234 |
| Popis: | We introduce the multiplexing of a crossing, replacing a classical crossing of a virtual link diagram with multiple crossings which is a mixture of classical and virtual. For integers $m_{i}$ $(i=1,\ldots,n)$ and an ordered $n$-component virtual link diagram $D$, a new virtual link diagram $D(m_{1},\ldots,m_{n})$ is obtained from $D$ by the multiplexing of all crossings. For welded isotopic virtual link diagrams $D$ and $D'$, $D(m_{1},\ldots,m_{n})$ and $D'(m_{1},\ldots,m_{n})$ are welded isotopic. From the point of view of classical link theory, it seems very interesting that $D(m_{1},\ldots,m_{n})$ could not be welded isotopic to a classical link diagram even if $D$ is a classical one, and new classical link invariants are expected from known welded link invariants via the multiplexing of crossings. Comment: 9 pages, 16 figures |
| Databáze: | OpenAIRE |
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