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Higher Contiguity Distance

Nilay Ekiz Yazici, Ayse Borat

Abstract

In this paper, we introduce the higher analogues of contiguity distance and its relations with simplicial Lusternik-Schnirelmann category and discrete topological complexity. Also we study the effects of geometric realisation and barycentric subdivision in the sense that how the geometric realisation of the simplicial maps and the induced simplicial maps on barycentric subdivisions affects higher contiguity distance.

Higher Contiguity Distance

Abstract

In this paper, we introduce the higher analogues of contiguity distance and its relations with simplicial Lusternik-Schnirelmann category and discrete topological complexity. Also we study the effects of geometric realisation and barycentric subdivision in the sense that how the geometric realisation of the simplicial maps and the induced simplicial maps on barycentric subdivisions affects higher contiguity distance.
Paper Structure (5 sections, 26 theorems, 51 equations)

This paper contains 5 sections, 26 theorems, 51 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Higher Contiguity Distance
  4. Barycentric Subdivision
  5. Acknowledgement

Key Result

Lemma 2.1

FMMV$K$ is edge-path connected simplicial complex iff any two constant simplicial maps $L\rightarrow K$ are in the same contiguity class.

Theorems & Definitions (62)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Lemma 2.1
  • Definition 2.4
  • Definition 2.5
  • Definition 2.6
  • Definition 2.7
  • Definition 2.8
  • Definition 2.9
  • ...and 52 more