On products in a real moment-angle manifold
arXiv:1410.5543
Abstract
In this paper we give a necessary and sufficient condition for a (real) moment-angle complex to be a topological manifold. The cup and cap products in a real moment-angle manifold are studied: the Poincaré duality via cap products is equivalent to the Alexander duality of the defining complex . Consequently, the cohomology ring (with coefficients integers) of a polyhedral product by pairs of disks and their bounding spheres is isomorphic to that of a differential graded algebra associated to , and the dimensions of the disks.
29 pages, 3 figures; the content of our previous preprint arXiv:1301.1518 is included and extended in this one; accepted in Journal of the Mathematical Society of Japan (JMSJ)