## Algebraic & Geometric Topology

### Surface links which are coverings over the standard torus

Inasa Nakamura

#### 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 11, Number 3 (2011), 1497-1540.

Dates
Revised: 1 March 2011
Accepted: 2 March 2011
First available in Project Euclid: 19 December 2017

https://projecteuclid.org/euclid.agt/1513715237

Digital Object Identifier
doi:10.2140/agt.2011.11.1497

Mathematical Reviews number (MathSciNet)
MR2821433

Zentralblatt MATH identifier
1230.57022

#### Citation

Nakamura, Inasa. Surface links which are coverings over the standard torus. Algebr. Geom. Topol. 11 (2011), no. 3, 1497--1540. doi:10.2140/agt.2011.11.1497. https://projecteuclid.org/euclid.agt/1513715237

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