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Motivic Toda brackets

Xiaowen Dong

Abstract

We construct Toda brackets in unstable motivic homotopy theory and prove some fundamental properties of them. Furthermore we construct some examples of motivic Toda brackets.

Motivic Toda brackets

Abstract

We construct Toda brackets in unstable motivic homotopy theory and prove some fundamental properties of them. Furthermore we construct some examples of motivic Toda brackets.
Paper Structure (13 sections, 47 theorems, 126 equations)

This paper contains 13 sections, 47 theorems, 126 equations.

Table of Contents

  1. Introduction
  2. Motivic Toda brackets
  3. Quillen equivalences
  4. Toda brackets
  5. Properties of Toda brackets
  6. Examples
  7. Rational functions and naive $\mathbb{A}^1$-homotopies
  8. Cogroup structure on $\mathbb{P}^1_{\mathbb{Z}}$
  9. Change of base points
  10. An unstable Hopf relation
  11. Appendix
  12. $\Delta$-generated spaces
  13. Complex realization

Key Result

Proposition 2.1.1

The global projective model structure on $\mathrm{Pre}_{\Delta}(S)$ is simplicial.

Theorems & Definitions (94)

  • Definition 1.0.1
  • Proposition 2.1.1
  • proof
  • Proposition 2.1.2
  • proof
  • Proposition 2.1.3
  • Lemma 2.1.4
  • proof
  • Lemma 2.1.5
  • proof
  • ...and 84 more