THE TURNED TORUS KNOT IN <font>S</font><sup>4</sup>

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  • JEFFREY BOYLE
    University of Wisconsin-La Crosse, Mathematics Department, La Crosse, Wisconsin 54601, USA

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<jats:p> A spun knotted torus in the 4-sphere is formed by rigidly sweeping a knotted curve along a circle. Alternately, as the knotted curve is swept along the circle we could give it a number of full turns (Dehn twists). We show the resulting knotted torus depends only on the knotted curve and whether the number of turns is even or odd. The even and odd turned spun tori have nondiffeomorphic complements. This is generalized in some cases to include twist spun turned torus knots. </jats:p>

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