Several number knots are defined including the five knots introduced by W. Jehne. The question of the splitting of the group extension of the Hilbert class field can be read off in terms of the triviality of these knots.
"A Note on Number Knots and the Splitting of the Hilbert Class Field." Taiwanese J. Math. 24 (2) 283 - 300, April, 2020. https://doi.org/10.11650/tjm/190703