Equivariantly slicing strongly negative amphichiral knots

Boyle, Keegan; Issa, Ahmad

doi:10.2140/agt.2024.24.897

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Equivariantly slicing strongly negative amphichiral knots

Keegan Boyle and Ahmad Issa

Algebraic & Geometric Topology 24 (2024) 897–918

DOI: 10.2140/agt.2024.24.897

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

Open Access made possible by participating institutions via Subscribe to Open.

Volume 24, issue 2 (2024)