Small Cover and Halperin-Carlsson Conjecture -II
Algebraic Topology
2010-10-26 v1 Combinatorics
Geometric Topology
Abstract
For a small cover Q^n and any principal (Z_2)^m-bundle M^n over Q^n, it was shown in a previous work of the author that the total sum of Z_2-Betti numbers of M^n is at least 2^m. In this paper, we prove that when M^n is connected, the total sum of Z_2-Betti numbers of such an M^n exactly equals 2^m if and only if M^n is homeomorphic to a product of spheres, and Q^n in this case must be a generalized real Bott manifold (or equivalent, Q^n is a small cover over a product of simplices).
Cite
@article{arxiv.1010.4929,
title = {Small Cover and Halperin-Carlsson Conjecture -II},
author = {Li Yu},
journal= {arXiv preprint arXiv:1010.4929},
year = {2010}
}
Comments
11 pages