The homotopy types of PU(3)– and PSp(2)–gauge groups
The homotopy types of PU(3)– and PSp(2)–gauge groups
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DOI：
10.2140/agt.2016.16.1813
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发表时间：
2016-07
影响因子：
0.7
通讯作者：
S. Hasui;D. Kishimoto;A. Kono;Takashi Sato
中科院分区：
文献类型：
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作者：
S. Hasui;D. Kishimoto;A. Kono;Takashi Sato
这个问题是由第三作者在[11]中提出的，他考虑了当G D SU. 2/和X D S时的情形，而这个问题最重要的情形是当G是紧李群时.设G是紧连通单李群.然后用3.G/π Z对S上的主G-丛进行了分类。记S上的主G-丛的规范群为Gk.G/，它被k2 Zk. G/分类.在Gk.G/上有几个分类结果，我们在这里回忆一下G秩为2的情况。Kono [11]，Hamanaka and Kono [5]，Theriault [17]证明了下列结果：
This problem was posed by the third-named author in [11], who considered the case when G D SU.2/ and X D S , and the most important case of the problem is when G is a compact Lie group. Let G be a compact connected simple Lie group. Then the principal G–bundle over S is classified by 3.G/ Š Z. We denote by Gk.G/ the gauge group of the principal G–bundle over S classified by k 2 ZŠ 3.G/. There are several classification results on Gk.G/, and we here recall the case when G is of rank 2. The following results are proved in Kono [11], Hamanaka and Kono [5], Theriault [17]: