Journal of the Mathematical Society of Japan

Surface links with free abelian groups


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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

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

First available in Project Euclid: 24 January 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

surface link link group triple point number


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

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