For an oriented surface link
,
we can take a satellite construction called a 2-dimensional braid over
,
which is a surface link in the form of a covering over
. We
demonstrate that 2-dimensional braids over surface links are useful for showing the
distinctness of surface links. We investigate nontrivial examples of surface links with
free abelian groups of rank two, concluding that their link types are infinitely
many.
Institute for Biology and
Mathematics of Dynamic Cellular Processes
Interdisciplinary Center for Mathematical Sciences
Graduate School of Mathematical Sciences
The University of Tokyo
3-8-1 Komaba, Tokyo 153-8914
Japan