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| Haken 3-Manifolds in Small Covers* |
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Citation： |
Lisu WU,Li YU.Haken 3-Manifolds in Small Covers*[J].Chinese Annals of Mathematics B,2023,44(4):549~560 |
| Page view： 1231
Net amount： 742 |
Authors： |
Lisu WU; Li YU |
Foundation： |
This work was supported by the National Natural Science Foundation of China (No. 11871266) and the Priority Academic Program Development of Jiangsu Higher Education Institutions. |
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| Abstract： |
The authors prove that a 3-dimensional small cover M is a Haken manifold if and only if M is aspherical or equivalently the underlying simple polytope is a flag polytope. In addition, they find that M being Haken is also equivalent to the existence of a Riemannian metric with non-positive sectional curvature on M. |
Keywords： |
Small cover, Haken manifold, Incompressible surface, Flag polytope |
Classification： |
57M50, 57N16, 57S17, 57S25 |
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