2023/08/03 by Xun Gong, Anthony Sanchez, Gong, Xun +1
Biochemistry, Genetics and Molecular Biology · Engineering · Mathematics · #37D40 (Primary) 32G146 (Secondary) #Advanced Materials and Mechanics #Cellular transport and secretion #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR)
paper · pdf · doi:10.48550/arxiv.2308.02082
openalex publication_date 2023/08/03 · openalex created_date 2023/08/08 · openalex updated_date 2026/07/28
We demonstrate the existence of a certain genus four origami whose Kontsevich--Zorich monodromy is arithmetic in the sense of Sarnak. The surface is interesting because its Veech group is as large as possible and given by SL(2,\mathbb Z). When compared to other surfaces with Veech group SL(2,\mathbb Z) such as the Eierlegendre Wollmichsau and the Ornithorynque, an arithmetic Kontsevich--Zorich monodromy is surprising and indicates that there is little relationship between the Veech group and monodromy group of origamis. Additionally, we record the index and congruence level in the ambient symplectic group which gives data on what can appear in genus 4.