Bull. Korean Math. Soc. 2023; 60(5): 1295-1298
Online first article August 23, 2023 Printed September 30, 2023
https://doi.org/10.4134/BKMS.b220657
Copyright © The Korean Mathematical Society.
Donghoon Jang
Pusan National University
It is known that the complex projective space $\mathbb{CP}^n$ admits a spin structure if and only if $n$ is odd. In this paper, we provide another proof that $\mathbb{CP}^{2m}$ does not admit a spin structure, by using a circle action.
Keywords: Spin structure, circle action, $\Hat{A}$-genus, fixed point
MSC numbers: 58C30, 58J20
Supported by: This work was supported by a 2-Year Research Grant of Pusan National University.
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