Small Cover and Halperin-Carlsson Conjecture -II
Abstract
For a small cover Qn and any principal (Z2)m-bundle Mn over Qn, it was shown in a previous work of the author that the total sum of Z2-Betti numbers of Mn is at least 2m. In this paper, we prove that when Mn is connected, the total sum of Z2-Betti numbers of such an Mn exactly equals 2m if and only if Mn is homeomorphic to a product of spheres, and Qn in this case must be a generalized real Bott manifold (or equivalent, Qn is a small cover over a product of simplices).
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