Small subdivisions of simplicial complexes with the metric topology

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...

Computational Topology Simplicial Complexes

In the first lecture, we looked at concepts from point set topology, the branch of topology that studies continuity from an analytical point of view. This view does not have a computational nature: we cannot represent infinite point sets or their associated infinite open sets on a computer. Starting with this lecture, we will look at concepts from another major branch of topology: combinatorial...

Topology Proceedings 11 (1986) pp. 177-208: COMPLETIONS OF METRIC SIMPLICIAL COMPLEXES BY USING l_p-NORMS

Topological approximation by small simplicial complexes

Given a point-cloud dataset sampled from an underlying geometric space X, it is often desirable to build a simplicial complex S approximating the geometric or topological structure of X. For example, recent techniques in automatic feature location depend on the ability to estimate topological invariants of X. These calculations can be prohibitively expensive if the number of cells in the approx...

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...