Homotopy types of gauge groups of $\mathrm{PU}(p)$-bundles over spheres
| Autor: | Rea, Simon |
|---|---|
| Rok vydání: | 2020 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We examine the relation between the gauge groups of $\mathrm{SU}(n)$- and $\mathrm{PU}(n)$-bundles over $S^{2i}$, with $2\leq i\leq n$, particularly when $n$ is a prime. As special cases, for $\mathrm{PU}(5)$-bundles over $S^4$, we show that there is a rational or $p$-local equivalence $\mathcal{G}_{2,k}\simeq_{(p)}\mathcal{G}_{2,l}$ for any prime $p$ if, and only if, $(120,k)=(120,l)$, while for $\mathrm{PU}(3)$-bundles over $S^6$ there is an integral equivalence $\mathcal{G}_{3,k}\simeq\mathcal{G}_{3,l}$ if, and only if, $(120,k)=(120,l)$. Comment: 12 pages |
| Databáze: | arXiv |
| Externí odkaz: |
|