论文标题
$ sp（n）$ - 量规组的同型类型$ s^{4m} $
The homotopy types of $Sp(n)$-gauge groups over $S^{4m}$
论文作者
论文摘要
令$ m $和$ n $为两个正整数，这样$ m <n $。用$ p_ {n，k} $表示主$ sp（n）$ - $ s^{4M} $和$ \ m nathcal {g} _ {k，m}（k，m}（sp（n））$是$ p_ {n，k} $的$ k { $π_{4M}（b（sp（n）））\ cong \ mathbb {z} $。在本文中，我们将通过给出$ \ Mathcal {g} _ {k，m}（sp（n））$的同质类型的分类，通过给出$ \ MATHCAL {G} _ {k，m}（sp（n））$的同型类型的下限。此外，在特殊情况下，$ sp（3）$ - 量规组超过$ s^8 $和$ sp（4）$ - 规格组，超过$ s^{12} $，我们为这些量规组的同型类型的数量提供了上限。
Let $m$ and $n$ be two positive integers such that $m < n$. Denote by $P_{n,k}$ the principal $Sp(n)$-bundle over $S^{4m}$ and $\mathcal{G}_{k,m}(Sp(n))$ be the gauge group of $P_{n,k}$ classified by $k\varepsilon'$, where $\varepsilon'$ is a generator of $π_{4m}(B(Sp(n)))\cong\mathbb{Z}$. In this article, we will partially classify the homotopy types of $\mathcal{G}_{k,m}(Sp(n))$ by giving a lower bound for the number of homotopy types of $\mathcal{G}_{k,m}(Sp(n))$. Also, in special cases $Sp(3)$-gauge groups over $S^8$ and $Sp(4)$-gauge groups over $S^{12}$ we give an upper bound for the number of homotopy types of these gauge groups.
