An instanton take on some knot detection results

Abstract

We give new proofs that Khovanov homology detects the figure eight knot and the cinquefoils, and that HOMFLY homology detects $5_2$ and each of the $P(-3,3,2n+1)$ pretzel knots. For all but the figure eight these mostly follow the same lines as in previous work. The key difference is that in honor of Tom Mrowka's 60th birthday, the arguments here use instanton Floer homology rather than knot Floer homology.

arXiv comment17 pages; written for the proceedings of "Frontiers in Geometry and Topology," a conference in honor of Tom Mrowka's 60th birthday. v2: accepted version

References in corpus (8)

• Matrix factorizations and link homology II
• Khovanov homology detects the trefoils
• Instanton Floer homology and the Alexander polynomial
• Branched covers of quasipositive links and L-spaces
• Instantons and L-space surgeries
• Khovanov homology detects the figure-eight knot
• Manifolds with small Heegaard Floer ranks
• The Khovanov homology of (p,-p,q) pretzel knots