Three flavors of twisted invariants of knots

Abstract

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 $L^2$-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 $L^2$-Alexander torsions and we conclude the paper with several conjectures on $L^2$-Alexander torsions.

26 pages

References in corpus (2)

• Floer homology and knot complements
• Twisted Alexander polynomials and a partial order on the set of prime knots

Cited by in corpus (1)

• Homotopy ribbon concordance, Blanchfield pairings, and twisted Alexander polynomials