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Operations on polyhedral products and a new topological construction of infinite families of toric manifolds (1011.0094v5)
Published 30 Oct 2010 in math.AT, math.AG, math.CO, and math.SG
Abstract: 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 which 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 literature.