Number of fixed points for unitary Tn−1-manifold

doi:10.1007/s11464-019-0785-5

Front. Math. China

2019, Vol. 14

Issue (4) : 819-831 https://doi.org/10.1007/s11464-019-0785-5

RESEARCH ARTICLE

Number of fixed points for unitary Tⁿ⁻¹-manifold

Shiyun WEN¹, Jun MA²(

)

¹. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
². College of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China

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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 $c ω T n − 1$ [M],where ω= (i₁, i₂, ..., i₆) are the multi-indexes for all i₁, i₂, ..., i₆∈ $ℕ$ . 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.

Keywords Unitary torus manifold equivariant Chern number cobordism localization theorem

Corresponding Author(s): Jun MA

Issue Date: 23 September 2019

Cite this article:

Shiyun WEN,Jun MA. Number of fixed points for unitary Tⁿ⁻¹-manifold[J]. Front. Math. China, 2019, 14(4): 819-831.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-019-0785-5
https://academic.hep.com.cn/fmc/EN/Y2019/V14/I4/819

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