Journal of the Mathematical Society of Japan

Surface links with free abelian groups

Inasa NAKAMURA

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Abstract

It is known that if a classical link group is a free abelian group, then its rank is at most two. It is also known that a $k$-component 2-link group ($k$ > 1) is not free abelian. In this paper, we give examples of $T^2$-links each of whose link groups is a free abelian group of rank three or four. Concerning the $T^2$-links of rank three, we determine the triple point numbers and we see that their link types are infinitely many.

Article information

Source
J. Math. Soc. Japan, Volume 66, Number 1 (2014), 247-256.

Dates
First available in Project Euclid: 24 January 2014

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1390600844

Digital Object Identifier
doi:10.2969/jmsj/06610247

Mathematical Reviews number (MathSciNet)
MR3161400

Zentralblatt MATH identifier
1297.57056

Subjects
Primary: 57Q45: Knots and links (in high dimensions) {For the low-dimensional case, see 57M25}
Secondary: 57Q35: Embeddings and immersions

Keywords
surface link link group triple point number

Citation

NAKAMURA, Inasa. Surface links with free abelian groups. J. Math. Soc. Japan 66 (2014), no. 1, 247--256. doi:10.2969/jmsj/06610247. https://projecteuclid.org/euclid.jmsj/1390600844


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