Three flavors of twisted invariants of knots

Original · EN

The Alexander polynomial of a knot has been generalized in three different ways to give twisted invariants. The resulting invariants are usually referred to as twisted Alexander polynomials, higher-order Alexander polynomials and L²-Alexander invariants of knots. We quickly recall the definitions and we summarize and compare some of their properties. We also report on work by the authors on L²-Alexander torsions and we conclude the paper with several conjectures on L²-Alexander torsions.