具有常余维数2k+7不动点集的(Z2)k作用

J4 ›› 2012, Vol. 50 ›› Issue (03): 439-.

具有常余维数2^k+7不动点集的(Z_2)^k作用

何江彦¹, 丁雁鸿², 冯杏芳¹

1. 军械工程学院基础部, |石家庄 050003|2. 河北师范大学数学与信息科学学院, 石家庄 050016

收稿日期:2011-06-07 出版日期:2012-05-26 发布日期:2012-05-28
通讯作者: 何江彦 E-mail:hezifan123@yahoo.com.cn

(Z₂)^kActions with Fixed Point Set of Constant Codimension 2^k+7

HE Jiangyan¹, DING Yanhong², FENG Xingfang¹

1. Department of Foundation, Ordnance Engineering College, Shijiazhuang 050003, China;
2. College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050016, China

Received:2011-06-07 Online:2012-05-26 Published:2012-05-28
Contact: HE Jiangyan E-mail:hezifan123@yahoo.com.cn

摘要/Abstract

摘要：

设(Z₂)^k作用于光滑闭流形Mⁿ上, 其不动点集具有常维数n-r, J^r_n,k是具有上述性质未定向的n维协边类［Mⁿ］构成的集合,
J^r_*,k=∑〖DD(〗〖〗n≥r〖DD)〗J^r_n,k为未定向协边环MO*=∑〖DD(〗〖〗n≥0〖DD)〗MO_n的理想. 通过构造MO*的一组生成元证明了J^2k+7_*,k(k≥5)由所有维数大于2^k+7且模2欧拉示性数为0的协边类及分解式中每个因子的维数都小于2^k的2^k+7维可分解协边类构成.

关键词: (Z²)_k作用, 协边类, 不动点集, 射影空间丛

Abstract:

Let Jrn,k denote the set of ndimensio
nal cobordism classes containing a representative Mn admitting a (Z2)
kaction with fixed point set of constant codimension r. Jr*,k=
∑〖DD(〗〖〗n≥r〖DD)〗Jrn,k is an idea of the unoriented cobordi
sm ring MO*=∑〖DD(〗〖〗n≥0〖DD)〗MOn. The authors constructed the special genera
tors of MO* to prove that J2k+7*,k(k≥5)
consists of all classes of dimension greater than 2k+7 with 0 mod 2 Euler
characteristic and the decomposables of dimension 2k+7 in which each
factor of monomials has dimension less than 2k.

Key words: (Z₂)^kaction, cobordism class, fixed point set, projective space bundle

中图分类号:

O189.3

何江彦, 丁雁鸿, 冯杏芳. 具有常余维数2^k+7不动点集的(Z_2)^k作用[J]. J4, 2012, 50(03): 439-.

HE Jiang-Pan, DING Yan-Hong, FENG Xing-Fang. (Z₂)^kActions with Fixed Point Set of Constant Codimension 2^k+7[J]. J4, 2012, 50(03): 439-.

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