Year: 2026
Type: preprint
Abstract: We prove that every Lawson surface $ξ_{k,l}\subset\mathbb S^3$ of genus $kl>1$ is non-algebraic: any real polynomial vanishing on $ξ_{k,l}$ vanishes identically on $\mathbb S^3$. This answers a question posed by Hsiang in 1967 and proves Lawson's 1970 conjecture for $ξ_{2,2}$. The proof uses a reflection principle for the monodromy of the associated family of flat connections.
Source: arXiv (Cornell University)
Authors: Heller, Lynn, Heller, Sebastian
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221822894