Surface links which are coverings over the standard torus

Nakamura, Inasa¹

¹Research Institute for Mathematical Sciences, Kyoto University, Oiwake-cho, Kitashirakawa, Sakyo-ku, Kyoto 606-8502, Japan

Algebraic and Geometric Topology, Tome 11 (2011) no. 3, pp. 1497-1540

Résumé

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.

Détail

DOI : 10.2140/agt.2011.11.1497

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

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