The Homotopy Types of $SU(4)$-Gauge Groups

Tyrone Cutler; Stephen Theriault

The Homotopy Types of $SU(4)$-Gauge Groups

Algebraic Topology 2022-06-28 v3

Authors: Tyrone Cutler , Stephen Theriault

Abstract

Let $\mathcal{G}_k$ be the gauge group of the principal $SU(4)$ -bundle over $S^4$ with second Chern class $k$ and let $p$ be a prime. We show that there is a rational or $p$ -local homotopy equivalence $\Omega\mathcal{G}_k\simeq\Omega\mathcal{G}_{k'}$ if and only if $(60,k)=(60,k')$ .

Keywords

gauge group su(4)-bundle homotopy equivalence chern class rational homotopy p-local homotopy

Cite

@article{arxiv.1909.04643,
  title  = {The Homotopy Types of $SU(4)$-Gauge Groups},
  author = {Tyrone Cutler and Stephen Theriault},
  journal= {arXiv preprint arXiv:1909.04643},
  year   = {2022}
}

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17 pages

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