Circle bundles over 4-manifolds

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Haibao Duan , Chao Liang This is my paper

classification math.GT math.AT

keywords admitsbundlescircleconnectedcoveringeverymanifoldmanifolds

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Every 1-connected topological 4-manifold M admits a $S^{1}$-covering by $#_{r-1}S^{2}\times S^{3}$, where $r=$rank$H^{2}(M;\QTR{Bbb}{Z})$.