English

The Kronecker-Weyl equidistribution theorem and geodesics in 3-manifolds

Number Theory 2022-05-18 v4

Abstract

Given any rectangular polyhedron 3-manifold PP tiled with unit cubes, we find infinitely many explicit directions related to cubic algebraic numbers such that all half-infinite geodesics in these directions are uniformly distributed in PP.

Keywords

Cite

@article{arxiv.2012.09464,
  title  = {The Kronecker-Weyl equidistribution theorem and geodesics in 3-manifolds},
  author = {Jozsef Beck and William Chen},
  journal= {arXiv preprint arXiv:2012.09464},
  year   = {2022}
}

Comments

The argument in this paper is based on an earlier result where we have discovered a major flaw in the argument