Showing distinctness of surface links by taking 2-dimensional braids

Abstract

For an oriented surface link $S$, we can take a satellite construction called a 2-dimensional braid over $S$, which is a surface link in the form of a covering over $S$. We demonstrate that 2-dimensional braids over surface links are useful for showing the distinctness of surface links. We investigate non-trivial examples of surface links with free abelian group of rank two, concluding that their link types are infinitely many.

14 pages, 5 figures, Title changed, Corollary 6.2 changed to Remark 2.4, Proof of Theorem 1.1 rewritten, to appear in Pacific J. Math

References in corpus (5)

• Surface links which are coverings over the standard torus
• Satellites of an oriented surface link and their local moves
• Surface links with free abelian link groups
• Triple linking numbers and triple point numbers of certain $T^2$-links
• On surface links whose link groups are abelian