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The 2-local homotopy types of G_2-gauge groups

Masaki Kameko

Abstract

We determine the 2-local homotopy types of G_2-gauge groups over S^4.

The 2-local homotopy types of G_2-gauge groups

Abstract

We determine the 2-local homotopy types of G_2-gauge groups over S^4.

Paper Structure

This paper contains 6 sections, 31 theorems, 65 equations.

Table of Contents

  1. Introduction
  2. Homotopy groups
  3. Proof of Proposition \ref{['proposition:1.5']}
  4. Proof of Proposition \ref{['proposition:3.1']}
  5. Proof of Proposition \ref{['proposition:3.10']}
  6. Proof of Proposition \ref{['proposition:1.2']}

Key Result

Theorem 1.1

Let $\mathcal{G}_k$ be the gauge group of a principal $G_2$-bundle over $S^4$ whose classifying map is $k\in \mathbb{Z}\cong \pi_{4}(BG_2)$. $\mathcal{G}_k\simeq_{(p)} \mathcal{G}_{k'}$ at any prime $p$ if and only if $(k, 168)=(k', 168)$.

Theorems & Definitions (56)

  • Theorem 1.1
  • Proposition 1.2
  • Proposition 1.3
  • Theorem 1.4
  • Proposition 1.5
  • proof : Proof of Proposition \ref{['proposition:1.3']}
  • Proposition 2.1
  • proof
  • Proposition 2.2
  • proof
  • ...and 46 more