RESEARCH ARTICLE

Number of fixed points for unitary Tn−1-manifold

  • Shiyun WEN 1 ,
  • Jun MA , 2
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  • 1. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
  • 2. College of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China

Received date: 24 Jun 2019

Accepted date: 03 Aug 2019

Published date: 15 Aug 2019

Copyright

2019 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature

Abstract

Let M be a 2n-dimensional closed unitary manifold with a Tn−1-action with only isolated fixed points. In this paper, we first prove that the equivariant cobordism class of a unitary Tn−1-manifold M is just determined by the equivariant Chern numbers cωTn1[M],where ω= (i1, i2, ..., i6) are the multi-indexes for all i1, i2, ..., i6. Then we show that if Mdoes 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.

Cite this article

Shiyun WEN , Jun MA . Number of fixed points for unitary Tn−1-manifold[J]. Frontiers of Mathematics in China, 2019 , 14(4) : 819 -831 . DOI: 10.1007/s11464-019-0785-5

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