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Equivariantly slicing strongly negative amphichiral knots

Keegan Boyle and Ahmad Issa

Algebraic & Geometric Topology 24 (2024) 897–918
Abstract

We prove obstructions to a strongly negative amphichiral knot bounding an equivariant slice disk in the 4–ball using the determinant, Spin c–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.

Keywords
knot theory, equivariantly slice knots, strongly negative amphichiral
Mathematical Subject Classification
Primary: 57K10, 57M60
References
Publication
Received: 2 October 2021
Revised: 23 July 2022
Accepted: 18 August 2022
Published: 12 April 2024
Authors
Keegan Boyle
Department of Mathematics
University of British Columbia
Vancouver, BC
Canada
Ahmad Issa
Department of Mathematics
University of British Columbia
Vancouver, BC
Canada

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