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 34 π 2 3 ⋅ 16 \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.