Small Cover and Halperin-Carlsson Conjecture

Details Small Cover and Halperin-Carlsson Conjecture Small Cover and Halperin-Carlsson Conjecture

2010-03-30

arxiv.org/abs/1003.5740v2

Mathematics

Algebraic Topology

20 pages, 4 figure. The article is significantly expanded from the previous version, and some references are added

Scientific paper

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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