Invariants of PL manifolds from metrized simplicial complexes. Three-dimensional case

Full Subcomplexes of CAT(0) Simplicial Complexes

In this article, I prove that full subcomplexes of CAT(0) simplicial 3-complexes inherit the non positive curvature condition, and describe a family of counterexamples that prove this result can not be extended to higher dimensions.

On simplicial and cubical complexes with short links

We consider closed simplicial and cubical $n$-complexes in terms of link of their $(n-2)$-faces. Especially, we consider the case, when this link has size 3 or 4, i.e., every $(n-2)$-face is contained in 3 or 4 $n$-faces. Such simplicial complexes with {\em short} (i.e. of length 3 or 4) links are completely classified by their {\em characteristic partition}. We consider also embedding into hypercubes of the skeletons of simplicial and cubical complexes.

Alexander猜想在无限单纯复形上的推广

Alexander's conjecture for infinite simplicial complexes

将Alexander猜想从有限单纯复形推广到无限单纯复形，证明任意两个具有共同子划分的无限三角剖分必有共同星形子划分。

On Codimension one Embedding of Simplicial Complexes

We study $d$-dimensional simplicial complexes that are PL embeddable in $\mathbb{R}^{d+1}$. It is shown that such a complex must satisfy a certain homological condition. The existence of this obstruction allows us to provide a systematic approach to deriving upper bounds for the number of top-dimensional faces of such complexes, particularly in low dimensions.

Non-commutative Simplicial Complexes and the Baum-Connes Conjecture

We associate a non-commutative $C^*$-algebra with any locally finite simplicial complex. We determine the $K$-theory of these algebras and show that they can be used to obtain a conceptual explanation for the Baum-Connes conjecture.

simpcomp -- A GAP toolbox for simplicial complexes

simpcomp is an extension (a so called package) to GAP, the well known system for computational discrete algebra. The package enables the user to compute numerous properties of (abstract) simplicial complexes, provides functions to construct new complexes from existing ones and an extensive library of triangulations of manifolds.