Volume 11, issue 3 (2011)

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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 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 2000
Primary: 57Q45
Secondary: 57Q35
References
Publication
Received: 25 June 2009
Revised: 1 March 2011
Accepted: 2 March 2011
Published: 26 May 2011
Authors
Inasa Nakamura
Research Institute for Mathematical Sciences
Kyoto University
Oiwake-cho, Kitashirakawa, Sakyo-ku
Kyoto 606-8502
Japan