Extension of the double-twist knot formulas to genus-one knots
Theorems concerning the ADO invariant and the relationship between CGP and WRT invariants are stated for double twist knots. A Seifert genus 1 knot is a knot whose Seifert genus is . Genus-one extension conjecture. The formulas of Theorems 2 and 3 should hold for any Seifert genus knot. This would extend the results from the two-parameter family of double twist knots to all genus-one knots; the statement is presented as an expected generalization, and no proof or resolution is given here.
References
Primary source
Anna Beliakova and Kazuhiro Hikami, “Non-semisimple invariants and Habiro's series”, arXiv:2009.13285 (2020).
Additional references
2 papers in this index state this conjecture (1998–2020). The statement above is taken from the most recent of them; the others are arXiv:math/9810073.
Progress summary
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