TY - JOUR
T1 - Link invariants derived from multiplexing of crossings
AU - Miyazawa, Haruko Aida
AU - Wada, Kodai
AU - Yasuhara, Akira
N1 - Funding Information:
The authors would like to thank Professor J Scott Carter for informing us of a result in [6] which helped us prove Theorem 3.2. We also warmly thank the referee for a careful reading of the manuscript and useful comments. This work was supported by JSPS KAKENHI Grant numbers JP26400098, JP17J08186, JP17K05264.
Publisher Copyright:
© 2018, Mathematical Sciences Publishers. All rights reserved.
PY - 2018/4/26
Y1 - 2018/4/26
N2 - 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.
AB - 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.
KW - Alexander polynomial
KW - Generalized link group
KW - Multiplexing of crossings
KW - Welded link
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U2 - 10.2140/agt.2018.18.2497
DO - 10.2140/agt.2018.18.2497
M3 - Article
AN - SCOPUS:85049163303
SN - 1472-2747
VL - 18
SP - 2497
EP - 2507
JO - Algebraic and Geometric Topology
JF - Algebraic and Geometric Topology
IS - 4
ER -