Some cellular subdivisions of simplicial complexes

Some Cellular Subdivisions of Simplicial Complexes

In a previous paper the author has associated with every inverse system of compact CW-complexes X with limit X and every simplicial complex K with geometric realization |K| a resolution of X × |K|, which consists of spaces having the homotopy type of polyhedra. In a subsequent paper it is shown that this construction is functorial. The proof depends essentially on particular cellular subdivisio...

Subdivisions of Toric Complexes

We introduce toric complexes as polyhedral complexes consisting of rational cones together with a set of integral generators for each cone, and we define their associated face rings. Abstract simplicial complexes and rational fans can be considered as toric complexes, and the face ring for toric complexes extends Stanley and Reisner’s face ring for abstract simplicial complexes [20] and Stanley...

New methods for constructing shellable simplicial complexes

A clutter $mathcal{C}$ with vertex set $[n]$ is an antichain of subsets of $[n]$, called circuits, covering all vertices. The clutter is $d$-uniform if all of its circuits have the same cardinality $d$. If $mathbb{K}$ is a field, then there is a one-to-one correspondence between clutters on $V$ and square-free monomial ideals in $mathbb{K}[x_1,ldots,x_n]$ as follows: To each clutter $mathcal{C}...

Minors of simplicial complexes

We extend the notion of a minor from matroids to simplicial complexes. We show that the class of matroids, as well as the class of independence complexes, is characterized by a single forbidden minor. Inspired by a recent result of Aharoni and Berger, we investigate possible ways to extend the matroid intersection theorem to simplicial complexes.

On Isomorphism of Simplicial Complexes and Their Related Algebras