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Classifications of 2-complexes whose finite fundamental group is that of a 3-manifold

Classifications of 2-complexes whose finite fundamental group is that of a 3-manifold

We consider spines of spherical space forms; i.e., spines of closed oriented 3-manifolds whose universal cover is the 3-sphere. We give sufficient conditions for such spines to be homotopy or simple homotopy equivalent to 2-complexes with the same fundamental group G and minimal Euler characteristic 1. If the group ring …