#### Volume 11, issue 3 (2011)

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1472-2739 ISSN (print): 1472-2747
Surface links which are coverings over the standard torus

### Inasa Nakamura

Algebraic & Geometric Topology 11 (2011) 1497–1540
##### Abstract

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 ${T}^{2}$–link is equivalent to the split union of spun ${T}^{2}$–links and turned spun ${T}^{2}$–links. We show that a certain torus-covering ${T}^{2}$–link has a nonclassical link group. We give a certain class of ribbon torus-covering ${T}^{2}$–links. We present the quandle cocycle invariant of a certain torus-covering ${T}^{2}$–link obtained from a classical braid, by using the quandle cocycle invariants of the closure of the braid.

##### Keywords
surface link, $2$–dimensional braid, knot group, triple point number, quandle cocycle invariant
Primary: 57Q45
Secondary: 57Q35