The $(2,1)$-cable of the figure-eight knot is not smoothly slice

Abhishek Mallick; Irving Dai; Junghwan Park; Matthew Stoffregen; Sungkyung Kang

The $(2,1)$-cable of the figure-eight knot is not smoothly slice

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arxiv 2207.14187 v2 pith:AQKJ5G3M submitted 2022-07-28 math.GT

Irving Dai , Sungkyung Kang , Abhishek Mallick , JungHwan Park , Matthew Stoffregen This is my paper · ORCID

classification math.GT

keywords cablefigure-eightknotslicesmoothlyballboundsbranched

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abstract

We prove that the $(2,1)$-cable of the figure-eight knot is not smoothly slice by showing that its branched double cover bounds no equivariant homology ball.

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Equivariant Q-sliceness of strongly invertible knots
math.GT 2024-12 conditional novelty 5.0 of 10

The paper introduces equivariant Q-sliceness for strongly invertible knots, proves Klein amphichiral knots are equivariant Q-slice in a single Q-homology 4-ball, and shows Alexander polynomial squareness obstructs it.

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