Algebraic & Geometric Topology 11 (2011) 1497–1540

DOI: 10.2140/agt.2011.11.1497

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 T²–link is equivalent to the split union of spun T²–links and turned spun T²–links. We show that a certain torus-covering T²–link has a nonclassical link group. We give a certain class of ribbon torus-covering T²–links. We present the quandle cocycle invariant of a certain torus-covering T²–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

Mathematical Subject Classification

Primary: 57Q45

Secondary: 57Q35

References

Publication

Received: 25 June 2009
Revised: 1 March 2011
Accepted: 2 March 2011
Published: 26 May 2011

Authors