2024/11/01 by Deblina Das, Das, Deblina, Arpan Kabiraj +1
Engineering · Computer Science · #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation #Digital Image Processing Techniques
paper · pdf · doi:10.48550/arxiv.2411.00481
In this article, we show that given any integer l≥ 2, every closed curve γ on the bouquet of n-circles Γ, admits a lift to a finite l-sheeted normal covering of Γ. Equivalently, identifying the free group Fn of n generators with the fundamental group of Γ, this statement asserts that Fn is a union of l-index normal subgroups for any l≥ 2. The proof proceeds by explicitly constructing families of l-sheeted normal coverings of Γ, together with a characterization, in terms of necessary and sufficient conditions, of when a closed curve γ on Γ lifts to these covers.