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arXiv · 1712.00698

Fundamental groups of small covers revisited

Lisu Wu·Li Yu
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Abstract

We study the topology of small covers from their fundamental groups. We find a way to obtain explicit presentations of the fundamental group of a small cover. Then we use these presentations to study the relations between the fundamental groups of a small cover and its facial submanifolds. In particular, we can determine when a facial submanifold of a small cover is $\pi_1$-injective in terms of some purely combinatorial data on the underlying simple polytope. In addition, we find that any 3-dimensional small cover has an embedded non-simply-connected $\pi_1$-injective surface. Using this result and some results of Schoen and Yau, we characterize all the 3-dimensional small covers that admit Riemannian metrics with nonnegative scalar curvature.

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Lisu Wu, Li Yu. 2017-12-03. Fundamental groups of small covers revisited. https://arxiv.org/abs/1712.00698

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