English

Small Cover and Halperin-Carlsson Conjecture

Algebraic Topology 2021-10-26 v2 Geometric Topology

Abstract

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.

Cite

@article{arxiv.1003.5740,
  title  = {Small Cover and Halperin-Carlsson Conjecture},
  author = {Li Yu},
  journal= {arXiv preprint arXiv:1003.5740},
  year   = {2021}
}

Comments

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

R2 v1 2026-06-21T15:04:20.830Z