English

Bounds on the number of non-simple closed geodesics on a surface

Geometric Topology 2017-02-21 v1

Abstract

We give bounds on the number of non-simple closed curves on a negatively curved surface, given upper bounds on both length and self-intersection number. In particular, it was previously known that the number of all closed curves of length at most LL grows exponentially in LL. We get exponentially tighter bounds given weak conditions on self-intersection number.

Keywords

Cite

@article{arxiv.1505.07171,
  title  = {Bounds on the number of non-simple closed geodesics on a surface},
  author = {Jenya Sapir},
  journal= {arXiv preprint arXiv:1505.07171},
  year   = {2017}
}