论文标题
$ \ mathrm {pu}（p）$ - 捆绑的量规类型的同型类型
Homotopy types of gauge groups of $\mathrm{PU}(p)$-bundles over spheres
论文作者
论文摘要
我们检查了$ \ mathrm {su}（n）$ - 和$ \ mathrm {pu}（n）$ - 捆绑$ s^{2i} $的量规组之间的关系，$ 2 \ leq i \ leq n $，尤其是当$ n $是$ n $时。作为特殊情况，对于$ \ mathrm {pu}（5）$ - 超过$ s^4 $，我们表明有一个理性的或$ p $ - 局部等价$ \ nathcal {g} _ {2，k}，k} \ k} \ simeq _ {（p）} {（p）}} $(120,k)=(120,l)$, 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, $(120,k)=(120,l)$.
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, $(120,k)=(120,l)$.
