Surface links with free abelian link groups

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.

10 pages, 6 figures, minor modifications, to appear in J. Math. Soc. Japan

References in corpus (2)

• Surface links which are coverings over the standard torus
• Triple linking numbers and triple point numbers of certain $T^2$-links

Cited by in corpus (4)

• Higher-form symmetries and 3-group in axion electrodynamics
• Global 3-group symmetry and 't Hooft anomalies in axion electrodynamics
• On surface links whose link groups are abelian
• Showing distinctness of surface links by taking 2-dimensional braids