We consider locally standard 2-torus manifolds, which are a generalization of small covers of Davis and Januszkiewicz and study their equivariant classification. We formulate a necessary and sufficient condition for two locally standard 2-torus manifolds over the same orbit space to be equivariantly homeomorphic. This leads us to count the equivariant homeomorphism classes of locally standard 2-torus manifolds with the same orbit space.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm115-2-3,
author = {Zhi L\"u and Mikiya Masuda},
title = {Equivariant classification of 2-torus manifolds},
journal = {Colloquium Mathematicae},
volume = {116},
year = {2009},
pages = {171-188},
zbl = {1165.57023},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm115-2-3}
}
Zhi Lü; Mikiya Masuda. Equivariant classification of 2-torus manifolds. Colloquium Mathematicae, Tome 116 (2009) pp. 171-188. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm115-2-3/