Knot Floer homology of some even 3-stranded pretzel knots

Abstract

We apply the theory of "peculiar modules" for the Floer homology of 4-ended tangles developed by Zibrowius (specifically, the immersed curve interpretation of the tangle invariants) to compute the Knot Floer Homology ($\widehat{HFK}$) of 3-stranded pretzel knots of the form $P(2a,-2b-1,\pm (2c+1))$ for positive integers $a,b,c$. This corrects a previous computation by Eftekhary; in particular, for the case of $P(2a,-2b-1,2c+1)$ where $b<c$ and $b<a-1$, it turns out the rank of $\widehat{HFK}$ is larger than that predicted by that work.

39 pages, 24 figures

References in corpus (2)

• Floer homology and knot complements
• Heegaard Floer homologies of pretzel knots