Coverings of Groups, Regular Dessins, and Surfaces
Jiyong Chen, Wenwen Fan, Cai Heng Li, Yan Zhou Zhu

TL;DR
This paper introduces a coset geometry approach to regular dessins and surfaces, characterizes face-quasiprimitive dessins as coverings of unicellular dessins, and explores coverings of simple groups, leading to new regular dessins.
Contribution
It provides a new geometric framework for understanding regular dessins and classifies face-quasiprimitive dessins as specific coverings, also initiating the study of Schur coverings of simple groups.
Findings
Three types of face-quasiprimitive regular dessins as coverings of unicellular dessins.
New constructions of regular dessins from these classifications.
Investigation of coverings between SL(2,p) and PSL(2,p) leading to Fibonacci dessins.
Abstract
A coset geometry representation of regular dessins is established, and employed to describe quotients and coverings of regular dessins and surfaces. A characterization is then given of face-quasiprimitive regular dessins as coverings of unicellular regular dessins. It shows that there are exactly three O'Nan-Scott-Praeger types of face-quasiprimitive regular dessins which are smooth coverings of unicellular regular dessins, leading to new constructions of interesting families of regular dessins. Finally, a problem of determining smooth Schur covering of simple groups is initiated by studying coverings between and , giving rise to interesting regular dessins like Fibonacci coverings.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsComputational Geometry and Mesh Generation · Advanced Graph Theory Research · Mathematics and Applications
