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 [8] (specifically, the immersed curve interpretation of the tangle invariants) to compute the Knot Floer Homology ( HF K) of 3-stranded pretzel knots of the form P (2a, −2b − 1, ±(2c + 1)) for positive integers a, b, c. This corrects a previous computation by Eftekhary [1]; 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 HF K is larger than that predicted by that work.