Sparse maps

TL;DR

This paper generalizes the Kolmogorov-Barzdin theorem for simplicial complex maps into Euclidean space, introducing sparse maps and exploring complexes with controlled 1-waist.

Contribution

It presents a new generalization of a classical theorem and introduces the concepts of sparse maps and controlled 1-waist in simplicial complexes.

Findings

Generalized Kolmogorov-Barzdin theorem for simplicial complexes

Introduction of sparse maps concept

Discussion of complexes with controlled 1-waist

Abstract

We prove a generalization of the Kolmogorov-Barzdin theorem for maps from simplicial complexes into Euclidean space. Along the way we introduce the notion of sparse maps and discuss maps from simplicial complexes with controlled 1-waist.