Full L2L^2-Alexander torsion conjecture for knot genus

About 12 years old · traced to

Let KK be an oriented knot. Full L2L^2-Alexander genus conjecture. The full L2L^2-Alexander torsion satisfies

deg⁡(τ(2)(K)(t))=2genus⁡(K)−1.\deg\left(\tau^{(2)}(K)(t)\right)=2\operatorname{genus}(K)-1.

This would make the full L2L^2-Alexander torsion a sharp genus invariant. The source reports partial evidence: for every oriented knot, an epimorphism onto a virtually abelian group is stated to attain the same degree, but the full conjecture remains open.

References

Primary source

Jérôme Dubois, Stefan Friedl and Wolfgang Lück, “Three flavors of twisted invariants of knots”, arXiv:1410.6924 (2014).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.