Operations on polyhedral products and a new topological construction of infinite families of toric manifolds

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.

This version includes improvements and corrections as suggested by the referee. The proof of Theorem 10.5 has been shortened considerably and a new reference has been added

References in corpus (4)

• The polyhedral product functor: a method of computation for moment-angle complexes, arrangements and related spaces
• Cup-products in generalized moment-angle complexes
• Doubling operation for polytopes and torus actions
• A generalization of the Davis-Januszkiewicz construction and applications to toric manifolds and iterated polyhedral products

Cited by in corpus (6)

• Composition of simplicial complexes, polytopes and multigraded Betti numbers
• Wedge operations and a new family of projective toric manifolds
• On products in a real moment-angle manifold
• Simplicial complexes Alexander dual to boundaries of polytopes
• The homotopy type of the polyhedral product for shifted complexes
• Exponential actions defined by vector configurations, Gale duality, and moment-angle manifolds