TY - JOUR T1 - Rational-Slice Knots via Strongly Negative-Amphicheiral Knots AU - Akio , Kawauchi JO - Communications in Mathematical Research VL - 2 SP - 177 EP - 192 PY - 2021 DA - 2021/06 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19304.html KW - rational-slice knot, strongly negative-amphicheiral knot, 0-surgery, rational cobordism, 4-manifold. AB -

We show that certain satellite knots of every strongly negative-amphicheiral rational knot are rational-slice knots. This proof also shows that the 0-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.