Year: 2026
Type: preprint
Abstract: We classify knot traces with trisection genus at most 2. We give infinitely many torus knots whose traces have trisection genus 3, and infinitely many hyperbolic knots whose traces have trisection genus 4. We also show that there exist infinite families of knots whose traces have arbitrarily large trisection genus. In addition, we determine or give sharp bounds for the trisection genus of the traces of several well-known knots, such as the figure-eight knot, the $(p, pq+1)$-torus knots, and the $(-2, 3, 2n+1)$-pretzel knots.
Source: arXiv (Cornell University)
Author: Takahashi, Natsuya
Institution: Nihon University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: トライセクションによる 4 次元多様体の微分構造の研究
OpenAlex ID: W7162761616