Distribution of periodic orbits in the homology group of a knot complement

2022/07/27 by Solly Coles, Coles, Solly, Richard R. Sharp +1
Computer Science · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2207.13608

openalex publication_date 2022/07/27 · openalex created_date 2023/02/13 · openalex updated_date 2026/07/28

Abstract

Consider a transitive Anosov flow on a closed 3-manifold. After removing a finite set of null-homologous periodic orbits, we study the distribution of the remaining periodic orbits in the homology of the knot complement.

Related

• Helicity, linking and the distribution of null-homologous periodic orbits for Anosov flows
• Counting periodic orbits of Anosov flows in free homotopy classes
• Infinitely many closed paths in the graph of Anosov flows
• Pairs of periodic orbits with fixed homology difference
• Existence of periodic orbits for sectional Anosov flows