Orientable hyperbolic 4-manifolds over the 120-cell

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 $\frac{34{\pi }^2}{3}\cdot 16$ 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.

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

References in corpus (6)

• Integral cohomology groups of real toric manifolds and small covers
• Multiplication structure of the cohomology ring of real toric spaces
• Hyperbolic Dehn filling in dimension four
• Compact hyperbolic manifolds without spin structures
• A four dimensional hyperbolic link complement in a standard $S^4$
• Surprising Examples of Manifolds in Toric Topology!