EQUIVARIANT Q-SLICENESS OF STRONGLY INVERTIBLE KNOTS
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, vol.379, no.5, pp.3693-3720, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 379 Issue: 5
- Publication Date: 2026
- Doi Number: 10.1090/tran/9559
- Journal Name: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
- Page Numbers: pp.3693-3720
- Middle East Technical University Affiliated: Yes
Abstract
We introduce and study the notion of equivariant Q-sliceness for strongly invertible knots. On the constructive side, we prove that every Klein amphichiral knot, which is a strongly invertible knot admitting a compatible negative amphichiral involution, is equivariant Q-slice in a single Q-homology 4-ball, by refining Kawauchi's construction and generalizing Levine's uniqueness result. On the obstructive side, we show that the equivariant version of the classical Fox-Milnor condition, proved recently by the first author [J. Topol. 17 (2024), 44 pp.], also obstructs equivariant Q-sliceness. We then introduce the equivariant Q-concordance group and study the natural maps between concordance groups as an application. We also list some open problems for future study.