Algebraic & Geometric Topology

Surface links which are coverings over the standard torus

Inasa Nakamura

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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

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

Received: 25 June 2009
Revised: 1 March 2011
Accepted: 2 March 2011
First available in Project Euclid: 19 December 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57Q45: Knots and links (in high dimensions) {For the low-dimensional case, see 57M25}
Secondary: 57Q35: Embeddings and immersions

surface link $2$–dimensional braid knot group triple point number quandle cocycle invariant


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.

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