2017/12/13 by Hambleton, Ian, Hillman, Jonathan A.
#57M60 #57N70 #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.1712.04572
We consider closed topological 4-manifolds M with universal cover S2×S2 and Euler characteristic χ(M) = 1. All such manifolds with π=π1(M)≅ \mathbb Z/4 are homotopy equivalent. In this case, we show that there are four homeomorphism types, and propose a candidate for a smooth example which is not homeomorphic to the geometric quotient. If π≅ \mathbb Z/2 × \mathbb Z/2, we show that there are three homotopy types (and between 6 and 24 homeomorphism types).