Braiding surface links which are coverings over the standard torus

Details Braiding surface links which are coverings over the standard torus Braiding surface links which are coverings over the standard torus

2009-05-10

arxiv.org/abs/0905.1469v2

Mathematics

Geometric Topology

25 pages, 22 figures. The main theorem is proved by using the motion picture method

Scientific paper

10.1142/S0218216512500113

We consider a surface link in the 4-space which can be presented by a simple branched covering over the standard torus, which we call a torus-covering link. Torus-covering links include spun $T^2$-knots and turned spun $T^2$-knots. In this paper we braid a torus-covering link over the standard 2-sphere. This gives an upper estimate of the braid index of a torus-covering link. In particular we show that the turned spun $T^2$-knot of the torus $(2,\,p)$-knot has the braid index four.

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