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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Link invariants derived from multiplexing of crossings

Haruko Aida Miyazawa, Kodai Wada and Akira Yasuhara

Algebraic & Geometric Topology 18 (2018) 2497–2507
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 mi (i = 1,,n) and an ordered n–component virtual link diagram D, a new virtual link diagram D(m1,,mn) is obtained from D by the multiplexing of all crossings. For welded isotopic virtual link diagrams D and D, the virtual link diagrams D(m1,,mn) and D(m1,,mn) 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