English

Orientable hyperbolic 4-manifolds over the 120-cell

Geometric Topology 2022-06-09 v4

Abstract

Since there is no hyperbolic Dehn filling theorem for higher dimensions, it is challenging to construct explicit hyperbolic manifolds of small volume in dimension at least four. Here, we build up closed hyperbolic 4-manifolds of volume 34π2316\frac{34\pi^2}{3}\cdot 16 by using the small cover theory. In particular, we classify all of the orientable four-dimensional small covers over the right-angled 120-cell up to homeomorphism; these are all with even intersection forms.

Keywords

Cite

@article{arxiv.1801.08814,
  title  = {Orientable hyperbolic 4-manifolds over the 120-cell},
  author = {Jiming Ma and Fangting Zheng},
  journal= {arXiv preprint arXiv:1801.08814},
  year   = {2022}
}

Comments

In this version, we corret some drawing typos in figures of adjacent matrices of $X_{45}$, $X_{55}$, $X_{56}$ and $X_{57}$. The author are grateful to Leonardo Ferrari who pointed out the mistakes

R2 v1 2026-06-22T23:58:05.882Z