English

Guts and The Minimal Volume Orientable Hyperbolic 3-Manifold with 3 Cusps

Geometric Topology 2023-04-21 v1

Abstract

The minimal volume of orientable hyperbolic manifolds with a given number of cusps has been found for 0,1,2,40,1,2,4 cusps, while the minimal volume of 3-cusped orientable hyperbolic manifolds remains unknown. By using guts in sutured manifolds and pared manifolds, we are able to show that for an orientable hyperbolic 3-manifold with 3 cusps such that every second homology class is libroid, its volume is at least 5.49=6×5.49\ldots = 6 \times Catalan's constant.

Keywords

Cite

@article{arxiv.2304.09950,
  title  = {Guts and The Minimal Volume Orientable Hyperbolic 3-Manifold with 3 Cusps},
  author = {Yue Zhang},
  journal= {arXiv preprint arXiv:2304.09950},
  year   = {2023}
}

Comments

40 pages, 10 figures. arXiv admin note: text overlap with arXiv:0804.0043, arXiv:1209.1374 by other authors

R2 v1 2026-06-28T10:11:41.401Z