Gluing formulas for the $L^2$-Alexander torsions

Abstract

We prove a Torres-like formula for the $L^2$-Alexander torsions of links, as well as formulas for connected sums and cablings of links. Along the way we compute explicitly the $L^2$-Alexander torsions of torus links inside the three-sphere, the solid torus and the thickened torus.

25 pages, 8 figures

References in corpus (4)

• Twisting $L^2$-invariants with finite-dimensional representations
• $L^2$-Alexander invariant for knots
• Degree of $L^2$-Alexander torsion for 3-manifolds
• The $L^2$-Alexander torsion for Seifert fiber spaces