Volume 25, Issue 2
Rational-Slice Knots via Strongly Negative-Amphicheiral Knots

Kawauchi Akio

Commun. Math. Res., 25 (2009), pp. 177-192.

Published online: 2021-06

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  • Abstract

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.

  • Keywords

rational-slice knot, strongly negative-amphicheiral knot, 0-surgery, rational cobordism, 4-manifold.

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COPYRIGHT: © Global Science Press

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@Article{CMR-25-177, author = {Akio , Kawauchi}, title = {Rational-Slice Knots via Strongly Negative-Amphicheiral Knots}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {25}, number = {2}, pages = {177--192}, abstract = {

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.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19304.html} }
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.

Kawauchi Akio. (2021). Rational-Slice Knots via Strongly Negative-Amphicheiral Knots. Communications in Mathematical Research . 25 (2). 177-192. doi:
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