Equivariant surgery with middle dimensional singular sets. I
Equivariant surgery with middle dimensional singular sets. I
复制标题
具有中维奇异集的等变手术。
DOI：
10.1515/form.1996.8.267
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
M. Morimoto
中科院分区：
文献类型：
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作者：
A. Bak;M. Morimoto
设G是一个nite群。让f：X！ Y 是维数为 2k = 6 的单连通、闭合、有向、光滑流形 X 和 Y 的 k 连通、1 次、G 框架映射。假设 G 对 X 的作用奇异集的维数至多为 k，我们构造一个阿贝尔群 W (G; Y ) 和一个元素 (f) 2 W (G; Y )，称为 f 的手术阻塞，使得 (f) 在 W (G; Y ) 中消失保证 f 可以通过 G-surgery 转换为同伦等价。致谢。我们希望对 I. Madsen 强调上述问题的重要性表示感谢。我们还感谢 E. Laitinen 和 K. Pawa lowski 对于修改手稿提出的建议。第二作者衷心感谢日本数学科学协会的支持以及日本文部科学省的科学研究补助金。
Let G be a nite group. Let f : X ! Y be a k-connected, degree 1, G-framed map of simply connected, closed, oriented, smooth manifolds X and Y of dimension 2k = 6. Under the assumption that the dimension of the singular set of the action of G on X is at most k, we construct an abelian group W (G; Y ) and an element (f) 2 W (G; Y ), called the surgery obstruction of f such that the vanishing of (f) in W (G; Y ) guarantees that f can converted by G-surgery to a homotopy equivalence. Acknowledgement. We wish to express our gratitude to I. Madsen for stressing the impor- tance of the problem above. We are also grateful to E. Laitinen and K. Pawa lowski for their suggestions concerning brushing up the manuscript. The second author gratefully acknowl- edges support by the Japan Association for Mathematical Sciences and a Grant-in-Aid for Scientic Research from the Ministry of Education, Science and Culture, Japan.