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Fundamental groups of small covers revisited. (arXiv:1712.00698v2 [math.AT] UPDATED)
来源于:arXiv
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 exactly when a facial submanifold of a small cover is
$\pi_1$-injective in terms of some purely combinatorial condition of the
underlying simple polytope. In addition, our study reveals some connections
between several topological notions for 3-dimensional small covers. This allows
us to determine when a 3-dimensional small cover and its regular
$Z_2^k$-covering spaces are Haken manifolds. 查看全文>>