Surface links which are coverings over the standard torus

Nakamura, Inasa

doi:10.2140/agt.2011.11.1497

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Surface links which are coverings over the standard torus

Inasa Nakamura

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 $T^{2}$ –link is equivalent to the split union of spun $T^{2}$ –links and turned spun $T^{2}$ –links. We show that a certain torus-covering $T^{2}$ –link has a nonclassical link group. We give a certain class of ribbon torus-covering $T^{2}$ –links. We present the quandle cocycle invariant of a certain torus-covering $T^{2}$ –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

Volume 11, issue 3 (2011)