The L²-Alexander invariant is stronger than the genus and the simplicial volume

Original · EN

We study how the genus, the simplicial volume and the L²-Alexander invariant of W. Li and W. Zhang can detect individual knots among all others. In particular, we use various techniques coming from hyperbolic geometry and topology to prove that the L²-Alexander invariant contains strictly more information than the pair (genus, simplicial volume). Along the way we prove that the L²-Alexander invariant detects the figure-eight knot 4₁, the twist knot 5₂ and an infinite family of cables on the figure-eight knot.