Braiding surface links which are coverings over the standard torus

Abstract

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.

arXiv comment25 pages, 22 figures. The main theorem is proved by using the motion picture method