This article gives a natural decomposition of the suspension of a generalized moment-angle complex or partial product space which arises as the polyhedral product functor described below. The introduction and application of the smash product moment-angle complex provides a precise identification of the stable homotopy type of the values of the polyhedral product functor. One direct consequence ...

This article gives a natural decomposition of the suspension of generalized moment-angle complexes or partial product spaces which arise as polyhedral product functors described below. In the special case of the complements of certain subspace arrangements, the geometrical decomposition implies the homological decomposition in Goresky-MacPherson [20], Hochster[22], Baskakov [3], Panov [36], and...

When do syzygies depend on the characteristic of field? Even for well-studied families examples, very little is known. For a family random monomial ideals, namely Stanley--Reisner ideals flag complexes, we prove that Betti numbers asymptotically almost always characteristic. Using this result, also develop heuristic dependence asymptotic algebraic varieties.

In computational complexity, a complexity class is given by a set of problems or functions, and a basic challenge is to show separations of complexity classes A 6= B especially when A is known to be a subset of B. In this paper we introduce a homological theory of functions that can be used to establish complexity separations, while also providing other interesting consequences. We propose to a...