Almost complex structures on spheres
Almost complex structures on spheres
复制标题
球体上几乎复杂的结构
DOI：
10.1016/j.difgeo.2017.10.010
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
M. Parton
中科院分区：
文献类型：
--
作者：
Panagiotis Konstantis;M. Parton
本文回顾了一个广为人知的事实，即只有S 2和S 6才是几乎复结构的球面。本文的证明使用了拓扑K-理论中的特征类和Bott周期定理。本文源于第二作者在2017年3月27日至3月30日在马尔堡举行的MAM1研讨会《(非)--S 6号上复杂结构的存在》上的演讲《球体上的几乎复杂结构》。这是一份审查文件，因此没有任何原创性的结果。我们试图做出一个清晰、有动机、尽可能自成一体的论述。
In this paper we review the well-known fact that the only spheres admitting an almost complex structure are S 2 and S 6. The proof described here uses characteristic classes and the Bott periodicity theorem in topological K-theory. This paper originates from the talk “Almost Complex Structures on Spheres” given by the second author at the MAM1 workshop “(Non)-existence of complex structures on S 6”, held in Marburg from March 27th to March 30th, 2017. It is a review paper, and as such no result is intended to be original. We tried to produce a clear, motivated and as much as possible self-contained exposition.