2025/01/24 by Julien Boulanger, Boulanger, Julien
Mathematics · Engineering · Computer Science · #Mathematics and Applications #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Computational Geometry and Mesh Generation
paper · pdf · doi:10.48550/arxiv.2501.14657
We study connection points on the double regular n-gon translation surface, for n ≥ 7 odd and its staircase model. For n ≠ 9, we provide a large family of points with coordinates in the trace field that are not connection points. This family includes the central points, and for n=7 we conjecture that all the remaining points are connection points. Further, in the case where n ≥ 7 is a prime number, we provide a constructive proof by exhibiting an explicit separatrix passing through a central point that does not extend to a saddle connection.