Year: 2026
Type: preprint
Abstract: We construct a multi-filtered smooth knot concordance invariant, $β(t^1, a, t^2)$, derived from the knot Floer complex $CFK^\infty$. $β$ is a three-variable piecewise linear function defined on $(0,2) \times \mathbb{R} \times (0,2)$. We demonstrate that $β$ satisfies a subadditivity relation. We apply $β$ to prove concordance results for a certain family of L-space knots. We show that the positive cones spanned by Teragaito's knots $K_{1,n}$ and $K_{2,n}$ are disjoint in the smooth concordance group $\mathcal{C}$. For positive L-space knots, we show $β$ completely determines the Alexander polynomial and distinguishes knots with identical $Υ$ invariants.
Source: arXiv (Cornell University)
Author: Umare, Kashti Satish
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214589514