Link invariants derived from multiplexing of crossings

Miyazawa, Haruko; Wada, Kodai; Yasuhara, Akira

doi:10.2140/agt.2018.18.2497

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Link invariants derived from multiplexing of crossings

Haruko Aida Miyazawa, Kodai Wada and Akira Yasuhara

Algebraic & Geometric Topology 18 (2018) 2497–2507

DOI: 10.2140/agt.2018.18.2497

Abstract

We introduce the multiplexing of a crossing, replacing a classical crossing of a virtual link diagram with a mixture of classical and virtual crossings.

For integers $m_{i}$ $(i = 1, \dots, n)$ and an ordered $n$ –component virtual link diagram $D$ , a new virtual link diagram $D (m_{1}, \dots, m_{n})$ is obtained from $D$ by the multiplexing of all crossings. For welded isotopic virtual link diagrams $D$ and $D^{'}$ , the virtual link diagrams $D (m_{1}, \dots, m_{n})$ and $D^{'} (m_{1}, \dots, m_{n})$ are welded isotopic. From the point of view of classical link theory, it seems very interesting that new classical link invariants are obtained from welded link invariants via the multiplexing of crossings.

Keywords

welded link, multiplexing of crossings, generalized link group, Alexander polynomial

Mathematical Subject Classification 2010

Primary: 57M25, 57M27

References

Publication

Received: 20 October 2017

Revised: 13 February 2018

Accepted: 7 March 2018

Published: 26 April 2018

Authors

Haruko Aida Miyazawa
Institute for Mathematics and Computer Science Tsuda University Tokyo Japan

Kodai Wada
Faculty of Education and Integrated Arts and Sciences Waseda University Tokyo Japan

Akira Yasuhara
Faculty of Commerce Waseda University Tokyo Japan

Volume 18, issue 4 (2018)