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.

17 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 (2)

• Instantons and L-space surgeries
• Khovanov homology detects the figure-eight knot