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Fundamental groups of small covers
[The 5th Korea Toric Topology Winter Workshop]
Date: 2019-01-22
Speaker : Lisu Wu (Fudan University)
Abstract : Davis and Januszkiewicz [Duke Math.J. 62(1911), pp. 417-451] proved that the fundamental group of a small cover is isomorphic to the kernel of a map from the associated Coxeter group to Zn2 , such description may not be sucient in some speci c problems. In this talk, I will describe this relation more explicitly based on the presentation of fundamental group we have calculated. Furthermore, our main result shows that the 1-injectivity of a facial submanifold of a small cover only depends on the local combinatorial structure of the corresponding face. This is a joint work with Li Yu.
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