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

TL;DR

This paper investigates how the periodic orbits of a transitive Anosov flow are distributed within the homology of a knot complement after removing certain null-homologous orbits, revealing insights into the flow's topological structure.

Contribution

It provides a detailed analysis of the distribution of periodic orbits in the homology of knot complements, extending understanding of Anosov flows in 3-manifolds.

Findings

Distribution patterns of periodic orbits in homology groups

Impact of removing null-homologous orbits on flow dynamics

New insights into the topology of Anosov flows in knot complements

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.