Number of fixed points for unitary T^n-1-manifold  

作　　者：Shiyun WEN Jun MA 

机构地区：[1]School of Mathematical Sciences, Capital Normal University, Beijing 100048, China [2]College of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China

出　　处：《Frontiers of Mathematics in China》2019年第4期819-831,共13页中国高等学校学术文摘·数学（英文）

摘　　要：Let M be a 2n-dimensional closed unitary manifold with a T^n-1- action with only isolated fixed points. In this paper, we first prove that the equivariant cobordism class of a unitary T^n-1-manifold M is just determined by the equivariant Chern numbers C^Tn-1/ω[M], where ω=(i1,i2,…,i6)are the multi-indexes for all i1,i2,…,i6∈N. Then we show that if M does not bound equivariantly, then the number of fixed points is greater than or equal to [n/6]+ 1, where [n/6] denotes the minimum integer no less than n/6.

关 键 词：UNITARY torus MANIFOLD EQUIVARIANT CHERN NUMBER COBORDISM localization theorem 

分 类 号：O[理学]