Equivariantly slicing strongly negative amphichiral knots

Keegan Boyle; Ahmad Issa

doi:10.2140/agt.2024.24.897

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arXiv · 2109.01198

Equivariantly slicing strongly negative amphichiral knots

Keegan Boyle·Ahmad Issa

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Abstract

We prove obstructions to a strongly negative amphichiral knot bounding an equivariant slice disk in the 4-ball using the determinant, Spinc-structures and Donaldson's theorem. Of the 16 slice strongly negative amphichiral knots with 12 or fewer crossings, our obstructions show that 8 are not equivariantly slice, we exhibit equivariant ribbon diagrams for 5 others, and the remaining 3 are unknown. Finally, we give an obstruction to a knot being strongly negative amphichiral in terms of Heegaard Floer correction terms.

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BibTeX RIS

Keegan Boyle, Ahmad Issa. 2021-09-02. Equivariantly slicing strongly negative amphichiral knots. https://doi.org/10.2140/agt.2024.24.897

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