Journal of the Mathematical Society of Japan

Classification of links up to self pass-move

Tetsuo SHIBUYA and Akira YASUHARA

Full-text: Open access

Abstract

A pass-move and a $\#$-move are local moves on oriented links defined by L. H. Kauffman and H. Murakami respectively. Two links are self pass-equivalent (resp. self $\#$-equivalent) if one can be deformed into the other by pass-moves (resp. #-moves), where none of them can occur between distinct components of the link. These relations are equivalence relations on ordered oriented links and stronger than link-homotopy defined by J. Milnor. We give two complete classifications of links with arbitrarily many components up to self pass-equivalence and up to self $\#$-equivalence respectively. So our classifications give subdivisions of link-homotopy classes.

Article information

Source
J. Math. Soc. Japan Volume 55, Number 4 (2003), 939-946.

Dates
First available in Project Euclid: 3 October 2007

Permanent link to this document
http://projecteuclid.org/euclid.jmsj/1191418757

Digital Object Identifier
doi:10.2969/jmsj/1191418757

Mathematical Reviews number (MathSciNet)
MR2003753

Zentralblatt MATH identifier
1046.57009

Subjects
Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}

Keywords
#-move pass-move link-homotopy Arf invariant

Citation

SHIBUYA, Tetsuo; YASUHARA, Akira. Classification of links up to self pass-move. J. Math. Soc. Japan 55 (2003), no. 4, 939--946. doi:10.2969/jmsj/1191418757. http://projecteuclid.org/euclid.jmsj/1191418757.


Export citation