Work

Embedded special Legendrian surfaces in $\mathbb S^5$

Year: 2026

Type: preprint

Abstract: We construct the first smooth embedded compact special Legendrian surfaces in $\mathbb S^5$ of genus greater than one. More precisely, for every sufficiently large integer $k$, we construct an embedded special Legendrian surface whose conformal structure is the Fermat curve of degree $k$ and genus $\tfrac12(k-1)(k-2)$. Our approach combines an elementary implicit function theorem with the description of special Legendrian surfaces via loop algebra-valued meromorphic connections and a characterization of the unitarizability locus in the ${SL}_{3}(\mathbb C)$-character variety of the thrice-punctured sphere.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2604.21521

Authors: Heller, Sebastian, Pedit, Franz, Ouyang, Charles

Institutions: Washington University in St. Louis, Beijing Institute of Mathematical Sciences and Applications, University of Massachusetts Amherst

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Stanley Medical Research Institute, Technische Universität Berlin

Award: PostDoctoral Research Fellowship

OpenAlex ID: W7155513404

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