Small Cover and Halperin-Carlsson Conjecture

Li Yu
Arxiv ID: 1003.5740Last updated: 10/26/2021
We prove that the Halperin-Carlsson conjecture holds for any free (Z_2)^m action on a compact manifold whose orbit space is a small cover. In addition, we show that if the total space of a principal (Z_2)^m bundle over a small cover is connected, it must be equivalent to a partial quotient of the corresponding real moment-angle manifold with some canonical Z_2-torus action.

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