On products in a real moment-angle manifold

Li Cai

On products in a real moment-angle manifold

Algebraic Topology 2015-11-03 v4

Authors: Li Cai

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 Poincar\'{e} duality via cap products is equivalent to the Alexander duality of the defining complex $K$ . 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 $K$ , and the dimensions of the disks.

Keywords

moment-angle manifold topological manifold cup product cap product Poincaré duality Alexander duality cohomology ring

Cite

@article{arxiv.1410.5543,
  title  = {On products in a real moment-angle manifold},
  author = {Li Cai},
  journal= {arXiv preprint arXiv:1410.5543},
  year   = {2015}
}

Comments

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)

On products in a real moment-angle manifold

Abstract

Keywords

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