Bukhshtaber, V. M.; Panov, T. E. Moment-angle complexes and combinatorics of simplicial manifolds. (English. Russian original) Zbl 0974.52013 Russ. Math. Surv. 55, No. 3, 567-569 (2000); translation from Usp. Mat. Nauk 55, No. 3, 171-172 (2000). This paper announces results, some of which have appeared elsewhere, and some of which will appear.By utilizing a cellular subdivision of the product of \(m\) 2-discs invariant under the action of an \(m\)-torus, the authors can analyze cubical decompositions determined by a simplicial structure. Their analyses for example lead to a description of the multiplicative structure of the cohomology of the complement of the coordinate subspaces of complex \(m\)-space.They are also able to recover the classical Dehn-Sommerville relations. Reviewer: Lee P.Neuwirth (Princeton) Cited in 1 Document MSC: 52B70 Polyhedral manifolds 57Q15 Triangulating manifolds 57R19 Algebraic topology on manifolds and differential topology Keywords:simplicial manifold; cubical decomposition; moment-angle complex; cohomology ring; Dehn-Sommerville relations × Cite Format Result Cite Review PDF Full Text: DOI arXiv