The Complement of Polyhedral Product Spaces and the Dual Simplicial Complexes

Abstract

In this paper, we define and prove basic properties of complement polyhedral product spaces, dual complexes and polyhedral product complexes. Then we compute the universal algebra of polyhedral product complexes under certain split conditions and the Alexander duality isomorphism on certain polyhedral product spaces.

33 pages. arXiv admin note: substantial text overlap with arXiv:1609.02291

References in corpus (2)

• Composition of simplicial complexes, polytopes and multigraded Betti numbers
• Discrete Morse theory for moment-angle complexes of pairs (D^n,S^{n-1})