2024/07/07 by Sivan Eldar, Eldar, Sivan, Stav Fahima +1
Mathematics · #37B99 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2407.05343
openalex publication_date 2024/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we provide a combinatorial tool to help study some topological properties of modular knots. We construct templates for the infinitely many Anosov flows on the trefoil complement, which are lifts of the geodesic flow on the modular surface, by lifting Ghys' modular template using self-covering of the trefoil complement of order 6k+1, for k∈ ℕ>0. This allows to study the knot properties of closed geodesics in these flows, and an explicit construction of an infinite family of links of two components with one of them being the trefoil, all commensurable to one another.