We show that certain satellite knots of every strongly negative-amphicheiral rational knot are rational-slice knots. This proof also shows that the O-surgery manifold of a certain strongly negative amphicheiral knot s...We show that certain satellite knots of every strongly negative-amphicheiral rational knot are rational-slice knots. This proof also shows that the O-surgery manifold of a certain strongly negative amphicheiral knot such as the figure-eight knot bounds a compact oriented smooth 4-manifold homotopy equivalent to the 2-sphere such that a second homology class of the 4-manifold is represented by a smoothly embedded 2-sphere if and only if the modulo two reduction of it is zero.展开更多
We obtain an equation among invariants obtained from the Alexander module of an amphicheiral link. For special cases, it deduces necessary conditions on the Alexander polynomial. By using the present results and some ...We obtain an equation among invariants obtained from the Alexander module of an amphicheiral link. For special cases, it deduces necessary conditions on the Alexander polynomial. By using the present results and some known results, we show that the Alexander polynomial of an algebraically split component- preservingly （±）-amphicheiral link with even components is zero, and we determine prime amphieheiral links with at least 2 components and up to 9 crossings.展开更多
文摘We show that certain satellite knots of every strongly negative-amphicheiral rational knot are rational-slice knots. This proof also shows that the O-surgery manifold of a certain strongly negative amphicheiral knot such as the figure-eight knot bounds a compact oriented smooth 4-manifold homotopy equivalent to the 2-sphere such that a second homology class of the 4-manifold is represented by a smoothly embedded 2-sphere if and only if the modulo two reduction of it is zero.
基金supported by National Natural Science Foundation of China (Grant No. 10801021/a010402)
文摘We obtain an equation among invariants obtained from the Alexander module of an amphicheiral link. For special cases, it deduces necessary conditions on the Alexander polynomial. By using the present results and some known results, we show that the Alexander polynomial of an algebraically split component- preservingly （±）-amphicheiral link with even components is zero, and we determine prime amphieheiral links with at least 2 components and up to 9 crossings.
