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

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

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

Geometric Topology 2024-09-04 v2

Authors: Irving Dai , Sungkyung Kang , Abhishek Mallick , JungHwan Park , Matthew Stoffregen

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.

Keywords

figure-eight knot (2,1)-cable smoothly slice branched double cover equivariant homology ball

Cite

@article{arxiv.2207.14187,
  title  = {The $(2,1)$-cable of the figure-eight knot is not smoothly slice},
  author = {Irving Dai and Sungkyung Kang and Abhishek Mallick and JungHwan Park and Matthew Stoffregen},
  journal= {arXiv preprint arXiv:2207.14187},
  year   = {2024}
}

Comments

14 pages; 5 figures. Final version; to appear in Inventiones Mathematicae

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

Abstract

Keywords

Cite

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