Study on characteristic numbers of G-manifolds and its fixed points submanifolds
Study on characteristic numbers of G-manifolds and its fixed points submanifolds
批准号:
17540082
负责人:
KOMIYA Katsuhiro
金额:
$2.18万
依托单位:
依托单位国家:
日本
项目类别:
Grant-in-Aid for Scientific Research (C)
财政年份:
2005
资助国家:
日本
项目状态:
已结题
起止时间:
2005 至 2006
中文摘要
1.剪切和粘贴操作定义了光滑G-流形集合上的等价关系,G是紧李群。这种关系称为SK-等价。SK-等价类的集合成为一个半环,其加法由不交并导出,乘积由两个G-流形的笛卡尔积导出。它的Grothendieck环称为G-流形的SK-环。当G是2阶循环群时,得到了SK-环可分解的一个充要条件。这里的可分解性意味着给定的G-流形是SK-等价于两个维数低于M的G-流形的乘积。利用G-流形及其不动点子流形的欧拉特征线得到了该条件.对于G的闭子群H,M^H表示M的受限制H-作用的不动点子流形。我们已经知道G-流形及其子流形的不动点的Euler特征线的各种算术同余。利用这些结果,我们得到如下事实:如果G是阿贝尔的,M是奇维的,M^G是0维的,即,若M^G由有限个孤立不动点组成,则M^G的点数为偶数。此外,如果G的指数为2的子群H是唯一的,则在不动点处的切表示作为H的表示彼此成对同构。
英文摘要
1. The cut-and-paste operation defines an equivalence relation on the set of smooth G-manifolds, G a compact Lie group. This relation is called SK-equivalence. The set of SK-equivalence classes becomes a semiring with the addition induced from the disjoint union and the product induced from the Cartesian product of two of G-manifolds. Its Grothendieck ring is called the SK-ring of G-manifolds. We obtain a necessary and sufficient condition for the decomposability in the SK-ring, if G is the cyclic group of order 2. Here the decomposability means for a given G-manifold to be Sk-equivalent to the product of two G-manifolds with a lower dimension than M. The condition is obtained in terms of the Euler characteristics of G-manifolds and its fixed points submanifolds.2. For a closed subgroup H of G, M^H denotes the fixed points submanifold of M by the restricted H-action. We already know various types of arithmetic congruences for the Euler characteristics of G-manifold and its fixed points submanoifolds. Making use of these results we obtain the following facts: if G is abelian, M is of odd-dimension, and M^G is of 0-dimension, i.e., M^G consists of finite isolated fixed points, then the number of points of M^G is even. Moreover, if the index 2 subgroup H of G is unique, then the tangential representations at fixed points are pairwisely isomorphic to each other as representations of H.
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DOI:
--
发表时间:
2006
期刊:
Journal of Mathematics of Kyoto University 46
影响因子:
--
作者:
[N.Iwase, M.Mimura, T.Nishimoto, S.Okuyama, 島川和久, Kohhei Yamaguchi, Kohhei Yamaguchi, Shigo Okuyama, Yoshifumi Ando, Yoshifumi Ando]
通讯作者:
Yoshifumi Ando
Nonexistence of homotopy equivalences which are C^∽ stable or of finite codimension
不存在 C^∽ 稳定或有限余维的同伦等价
DOI:
--
发表时间:
2006
期刊:
Topology and its applications 135
影响因子:
--
作者:
[N.Iwase, M.Mimura, T.Nishimoto, S.Okuyama, 島川和久, Kohhei Yamaguchi, Kohhei Yamaguchi, Shigo Okuyama, Yoshifumi Ando, Yoshifumi Ando, Yasuyuki Miyazawa, Y.Ando]
通讯作者:
Y.Ando
DOI:
10.1142/s0218216506005135
发表时间:
2006-12
期刊:
Journal of Knot Theory and Its Ramifications
影响因子:
0.5
作者:
[Y. Miyazawa]
通讯作者:
Y. Miyazawa
DOI:
10.1007/s00208-005-0646-2
发表时间:
2005-04
期刊:
Mathematische Annalen
影响因子:
1.4
作者:
[J. Berndt;J. Eschenburg;H. Naitoh;K. Tsukada]
通讯作者:
J. Berndt;J. Eschenburg;H. Naitoh;K. Tsukada
Nonexistence of homotopy equivalences which are C^∞ stable or of finite codimension
不存在 C^∞ 稳定或有限余维的同伦等价
DOI:
--
发表时间:
2006
期刊:
Topology and its applications 153
影响因子:
--
作者:
[N.Iwase, M.Mimura, T.Nishimoto, S.Okuyama, 島川和久, Kohhei Yamaguchi, Kohhei Yamaguchi, Shigo Okuyama, Yoshifumi Ando]
通讯作者:
Yoshifumi Ando
共 10 条
Research on families of fixed point sets of G-manifolds in transformation group theory
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批准号:15540079
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项目类别:Grant-in-Aid for Scientific Research (C)
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资助金额:$2.3万
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财政年份:2003
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负责人:KOMIYA Katsuhiro
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依托单位:
Study on Transformation Group Theory and Equivariant K-theory
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批准号:12640075
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项目类别:Grant-in-Aid for Scientific Research (C)
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资助金额:$0.9万
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财政年份:2000
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负责人:KOMIYA Katsuhiro
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依托单位:
Transformation Group Theory and Critical Point Theory
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批准号:09640113
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项目类别:Grant-in-Aid for Scientific Research (C)
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资助金额:$1.73万
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财政年份:1997
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负责人:KOMIYA Katsuhiro
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依托单位:
海外基金