报告摘要：
| A hyperbolic manifold is a manifold $M$ with a complete sectional curvature $-1$ Riemannian metric of finite volume. Since there is no hyperbolic Dehn filling theorem in higher dimensions, it is difficult to construct concrete hyperbolic manifolds of small volume in dimension at least four. We build up a census of closed hyperbolic 4-manifolds of volume $frac{34pi^2}{3}cdot 16$ by using small cover theory over the right-angled 120-cell. In particular, we classify all the orientable 4-dimensional small covers over the 120-cell and obtain exactly 56 many up to homeomorphism. Moreover, we calculate the homologies of the obtained orientable closed hyperbolic 4-manifolds and all of them have even intersection forms. This is a joint work with Fangting Zheng.
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