Simplicial approximation and complexity growth

2010/06/30 by Daniel J. Pons, Pons, Daniel J.
Mathematics · #Advanced Topology and Set Theory #Combinatorics #Computer science #Differential Geometry (math.DG) #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematics #Mathematics and Applications #math.DG

paper · pdf · doi:10.48550/arxiv.1006.5889

published in arXiv (Cornell University) (Cornell University) · Final version. Warning: peer rejected

openalex publication_date 2010/06/30 · arxiv created 2012/05/21 · arxiv updated 2012/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This work is motivated by two problems: 1) The approach of manifolds and spaces by triangulations. 2) The complexity growth in sequences of polyhedra. Considering both problems as related, new criteria and methods for approximating smooth manifolds are deduced. When the sequences of polyhedra are obtained by the action of a discrete group or semigroup, further control is given by geometric, topologic and complexity observables. We give a set of relevant examples to illustrate the results, both in infinite and finite dimensions.

Citations

• Metric Structures for Riemannian and Non-Riemannian Spaces
• Calibrated geometries

Related

• From the discrete to the continuous, from simplicial complexes to Riemannian manifolds. Approximating flows and cuts on manifolds by discrete versions
• Higher analogs of simplicial and combinatorial complexity
• Generating Simplicial Complexes
• Higher Contiguity Distance
• Simplicial Distance