We introduce a new construction of a surface link in 4–space. We construct a surface link as a branched covering over the standard torus, which we call a torus-covering link. We show that a certain torus-covering –link is equivalent to the split union of spun –links and turned spun –links. We show that a certain torus-covering –link has a nonclassical link group. We give a certain class of ribbon torus-covering –links. We present the quandle cocycle invariant of a certain torus-covering –link obtained from a classical braid, by using the quandle cocycle invariants of the closure of the braid.
"Surface links which are coverings over the standard torus." Algebr. Geom. Topol. 11 (3) 1497 - 1540, 2011. https://doi.org/10.2140/agt.2011.11.1497