EQUIVARIANT Q-SLICENESS OF STRONGLY INVERTIBLE KNOTS

Date

2025-12-23

Author

Di Prisa, Alessio
Şavk, Oğuz

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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.

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https://hdl.handle.net/11511/118536

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Department of Mathematics, Article