3 problems

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Lück's continuity conjecture for the twisted $L^2$ -Alexander torsion
Lück's continuity conjecture. The function $A^{(2)}(N,\psi,t)$ is continuous with respect to $(\psi,t)\in H^1(N;\mathbb{R})\times\mathbb{R}^+$ .
Conjecturesolved3-manifolds alexander-torsion l2-torsionarXiv posted 2 days ago
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Regularity conjecture for $L^2$ -Alexander torsion
Let $K$ be an oriented knot, let $\pi_K$ denote its knot group, and let $\gamma\colon\pi_K\to\Gamma$ be an admissible epimorphism. $L^2$ -Alexander torsion regularity conjecture. Th…
Conjectureopenalexander-torsion knot-theory l2-invariantsarXiv posted 2 days ago
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The full $L^2$ -Alexander torsion conjecture for genus, fiberedness and monodromy entropy
Let $K$ be a knot. The full $L^2$ -Alexander torsion conjecture. (1) The full $L^2$ -Alexander torsion $d70f^{(2)}(K)(t)$ determines the genus of $K$ . (2) The full $L^2$ -Alexander to…
Conjectureopenalexander-torsion knot-theory l2-invariantsarXiv posted 2 days ago

Lück's continuity conjecture for the twisted L2L^2L2-Alexander torsion