On Combinatorial Topology

Combinatorial Differential Topology and Geometry

A variety of questions in combinatorics lead one to the task of analyzing the topology of a simplicial complex, or a more general cell complex. However, there are few general techniques to aid in this investigation. On the other hand, the subjects of differential topology and geometry are devoted to precisely this sort of problem, except that the topological spaces in question are smooth manifo...

Combinatorial Topology and Distributed Computing

Distributed Computing Through Combinatorial Topology

Combinatorial Topology in Documents Clustering

This paper presents a novel approach to document clustering based on some geometric structure in Combinatorial Topology. Given a set of documents, the set of associations among frequently co-occurring terms in documents forms naturally a simplicial complex. The thesis is each connected component of this simplicial complex represents a primitive concept in the collection. Based on these primitiv...

Topology of Combinatorial Diierential Manifolds

We prove that all combinatorial diierential manifolds involving only Euclidean oriented matroids are PL manifolds. In doing so we introduce a new notion of triangulations of oriented matroids, and show that any triangulation of a Euclidean oriented matroid is a PL sphere. In Section 5 we adapt these results to get a new deenition of tri-angulations of oriented matroid polytopes, and show that a...