数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (3): 1021-1034.doi: 10.1016/S0252-9602(12)60076-9

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INVOLUTIONS FIXING ∪mi=1CPi(1) ×|HPi(n)

赵素倩1,2|王彦英1*   

  1. 1. College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050016, China;
    2. College of Sciences, Hebei University of Science and Technology, Shijiazhuang 050018, China
  • 收稿日期:2010-05-31 出版日期:2012-05-20 发布日期:2012-05-20
  • 通讯作者: 王彦英，wyanying2003@yahoo.com.cn E-mail:wyanying2003@yahoo.com.cn
  • 基金资助:

    This work is supported by NSFC (10971050; 11001073; 10901045), HNSFC(A2010000828), and FHUST (XL201043; QD201021).

INVOLUTIONS FIXING ∪mi=1CPi(1) ×|HPi(n)

 ZHAO Su-Qian1,2, WANG Yan-Ying1*   

  1. 1. College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050016, China;
    2. College of Sciences, Hebei University of Science and Technology, Shijiazhuang 050018, China
  • Received:2010-05-31 Online:2012-05-20 Published:2012-05-20
  • Contact: WANG Yan-Ying，wyanying2003@yahoo.com.cn E-mail:wyanying2003@yahoo.com.cn
  • Supported by:

    This work is supported by NSFC (10971050; 11001073; 10901045), HNSFC(A2010000828), and FHUST (XL201043; QD201021).

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摘要：

Let (M, T) be a closed manifold with an involution T. The fixed point set of T is F. In this article, bordism classes of the involutions with fixed point set F =∪mi=1CPi(1) × HPi(n) are determined, where CP(1) and HP(n) denote the 1-dimensional complex projective space and n-dimensional quaternionic projective space respectively, and n = 2p− 2 or n = 2p− 1 (p > 1).

关键词: Involution, bordism, fixed point set, Stiefel-Whitney class

Abstract:

Let (M, T) be a closed manifold with an involution T. The fixed point set of T is F. In this article, bordism classes of the involutions with fixed point set F =∪mi=1CPi(1) × HPi(n) are determined, where CP(1) and HP(n) denote the 1-dimensional complex projective space and n-dimensional quaternionic projective space respectively, and n = 2p− 2 or n = 2p− 1 (p > 1).

Key words: Involution, bordism, fixed point set, Stiefel-Whitney class

中图分类号: 

  • 57R85
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