On the connected sums of the $(2,1)$-cable of the figure eight knot

Yoshihiro Fukumoto; Masaki Taniguchi

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arXiv · 2501.07910

On the connected sums of the $(2,1)$-cable of the figure eight knot

Yoshihiro Fukumoto·Masaki Taniguchi

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Abstract

We show that the 3-fold (resp. 6-fold) connected sum of the $(2,1)$-cable of the figure-eight knot cannot bound a smooth null-homologous disk in a punctured $S^2 \times S^2$ (resp. in a punctured $#_2 S^2 \times S^2$. This result is obtained using a real version of the $10/8$-inequality established by Konno, Miyazawa, and Taniguchi.

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BibTeX RIS

Yoshihiro Fukumoto, Masaki Taniguchi. 2025-01-14. On the connected sums of the $(2,1)$-cable of the figure eight knot. https://arxiv.org/abs/2501.07910

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