Twisting, Stabilization and Bordered Floer homology

2025/07/20 by Azarpendar, Soheil
#57K18 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2507.15144

Abstract

Consider an unknot c in S³ and a knot K in S³-N(c). Twisting the knot K along c, or equivalently applying (1)/(m)-surgery on c, produces a family of knots \K_m\_{m ∈ ℤ}. We use bordered Floer homology and the theory of immersed curve invariants to show that for |m|≫0, total dimension of \widehatHFK(K_m), τ(K_m) and thickness of K_m are linear functions of m. Furthermore, we prove that the extremal coefficients of the Alexander polynomial and extremal knot Floer homologies of K_m stabilize as m goes to infinity. This generalizes results of Chen, Lambert-Cole, Roberts, Van Cott and the author on coherent twist families.

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