Lyapunov Maps, Simplicial Complexes and the Stone Functor

Cohen-Macaulay-ness in codimension for simplicial complexes and expansion functor

In this paper we show that expansion of a Buchsbaum simplicial complex is $CM_t$, for an optimal integer $tgeq 1$. Also, by imposing extra assumptions on a $CM_t$ simplicial complex, we provethat it can be obtained from a Buchsbaum complex.

An introduction to simplicial sets

This is an elementary introduction to simplicial sets, which are generalizations of ∆-complexes from algebraic topology. The theory of simplicial sets provides a way to express homotopy and homology without requiring topology. This paper is meant to be accessible to anyone who has had experience with algebraic topology and has at least basic knowledge of category theory. An important part of si...

Vertex Decomposable Simplicial Complexes Associated to Path Graphs

Introduction Vertex decomposability of a simplicial complex is a combinatorial topological concept which is related to the algebraic properties of the Stanley-Reisner ring of the simplicial complex. This notion was first defined by Provan and Billera in 1980 for k-decomposable pure complexes which is known as vertex decomposable when . Later Bjorner and Wachs extended this concept to non-pure ...

On Isomorphism of Simplicial Complexes and Their Related Algebras

An Introduction to Simplicial Sets

Simplicial sets, and more generally simplicial objects in a given category, are central to modern mathematics. While I am not a mathematical historian, I thought I would describe in conceptual outline how naturally simplicial sets arise from the classical study of simplicial complexes. I suspect that something like this recapitulates the historical development. We have described simplicial comp...