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On the higher rational topological complexity of certain elliptic spaces

Said Hamoun

Abstract

Through this paper, we show that $\text{TC}_r(Z)\leq r\cdot \text{cat}(Z)+χ_π(Z)$, for any simply-connected elliptic space $Z$ admitting a pure minimal Sullivan model with a differential of constant length. Here $χ_π(Z)$ denotes the homotopy characteristic and $r$ is an integer greater or equals than $2$. We also give a lower bound for $\text{TC}_r$ in the framework of coformal spaces and we compute the exact value of $\text{TC}_r$ for certain families of spaces.

On the higher rational topological complexity of certain elliptic spaces

Abstract

Through this paper, we show that , for any simply-connected elliptic space admitting a pure minimal Sullivan model with a differential of constant length. Here denotes the homotopy characteristic and is an integer greater or equals than . We also give a lower bound for in the framework of coformal spaces and we compute the exact value of for certain families of spaces.

Paper Structure

This paper contains 7 sections, 14 theorems, 46 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. The higher rational topological complexity of formal spaces
  4. An upper bound of the higher rational topological complexity of certain pure elliptic spaces
  5. The coformal case
  6. Acknowledgements

Key Result

Theorem 1

Let $(\Lambda V,d)$ be a pure elliptic minimal model which is formal. Then

Theorems & Definitions (26)

  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Theorem 4
  • Theorem 5
  • proof
  • proof
  • Theorem 8
  • proof
  • Theorem 9
  • ...and 16 more