Homology, Homotopy and Applications
Volume 17 (2015)
Operations on polyhedral products and a new topological construction of infinite families of toric manifolds
Pages: 137 – 160
A combinatorial construction is used to analyze the properties of polyhedral products  and generalized moment-angle complexes with respect to certain operations on CW pairs including exponentiation. This allows for the construction of infinite families of toric manifolds, associated to a given one, in a way that simplifies the combinatorial input and, consequently, the presentation of the cohomology rings. The new input is the interaction of a purely combinatorial construction with natural associated geometric constructions related to polyhedral products and toric manifolds. Applications of the methods and results developed here have appeared in [24, 25, 15, 18, 10, 23], and .
polyhedral product, moment-angle complex, moment-angle manifold, quasitoric manifold, toric manifold, quasitoric manifold, smooth toric variety, non-singular toric variety, fan, simplicial wedge, join
2010 Mathematics Subject Classification
Primary 13F55, 14M25, 52B11, 55N10, 55U10. Secondary 14F45, 55T10.