English

Hyperbolic 3-manifolds of low cusp volume

Geometric Topology 2021-09-30 v1

Abstract

We classify the complete hyperbolic 3-manifolds admitting a maximal cusp of volume at most 2.62. We use this to show that the figure-8 knot complement is the unique 1-cusped hyperbolic 3-manifold with nine or more non-hyperbolic fillings; to show that the figure-8 knot complement and its sister are the unique hyperbolic 3-manifolds with minimal volume maximal cusps; and to extend results on determining low volume closed and cusped hyperbolic 3-manifolds.

Keywords

Cite

@article{arxiv.2109.14570,
  title  = {Hyperbolic 3-manifolds of low cusp volume},
  author = {David Gabai and Robert Haraway and Robert Meyerhoff and Nathaniel Thurston and Andrew Yarmola},
  journal= {arXiv preprint arXiv:2109.14570},
  year   = {2021}
}

Comments

79 pages, 18 figures