The Cohomology Algebra of Polyhedral Product Objects
arXiv:1804.07907
Abstract
In this paper, we compute the homology group and cohomology algebra of various polyhedral product objects uniformly from the point of view of diagonal tensor product. As applications, we introduce the polyhedral product method into commutative algebra and show that the homotopy types of polyhedral product spaces depend on not only the homotopy type of each summand pair but also on the character coproduct of the pair.
108pages
References in corpus (5)
- The polyhedral product functor: a method of computation for moment-angle complexes, arrangements and related spaces
- Composition of simplicial complexes, polytopes and multigraded Betti numbers
- Discrete Morse theory for moment-angle complexes of pairs (D^n,S^{n-1})
- The homology of simpicial complements and the cohomology of moment-angle complexes
- Cellular cochain algebras and torus actions