Nonfibering spherical 3-orbifolds
Nonfibering spherical 3-orbifolds
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DOI：
10.1090/s0002-9947-1994-1118824-6
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发表时间：
1994
影响因子：
1.3
通讯作者：
W. Dunbar
中科院分区：
文献类型：
--
作者：
W. Dunbar
． 在SO(4)的有限子群中，正好有21个共轭类的成员作用于S3，使S3不被圆颤动。我们确定了相应的球面3-轨道，即对于每一个这样的G < SO(4)，我们在拓扑空间S3/G中描述了嵌入的三价图{x€S3: 31 /G e G s.t. G (x) = x}/G（在所有情况下都是S3同胚的）。明确的基本域（狄利克雷型）描述了9组，连同识别在边界上。剩下的12个球面轨道是作为它们的镜像或（分支）覆盖物得到的。
. Among the finite subgroups of SO(4), members of exactly 21 conjugacy classes act on S3 preserving no fibration of S3 by circles. We identify the corresponding spherical 3-orbifolds, i.e., for each such G < SO(4), we describe the embedded trivalent graph {x € S3 : 31 / g e G s.t. g(x) = x}/G in the topological space S3/G (which turns out to be homeomorphic to S3 in all cases). Explicit fundamental domains (of Dirichlet type) are described for 9 of the groups, together with the identifications to be made on the boundary. The remaining 12 spherical orbifolds are obtained as mirror images or (branched) covers of these.