首页    期刊浏览 2024年12月12日 星期四
登录注册

文章基本信息

  • 标题:Stable homotopy groups of spheres
  • 本地全文:下载
  • 作者:Daniel C. Isaksen ; Guozhen Wang ; Zhouli Xu
  • 期刊名称:Proceedings of the National Academy of Sciences
  • 印刷版ISSN:0027-8424
  • 电子版ISSN:1091-6490
  • 出版年度:2020
  • 卷号:117
  • 期号:40
  • 页码:24757-24763
  • DOI:10.1073/pnas.2012335117
  • 出版社:The National Academy of Sciences of the United States of America
  • 摘要:We discuss the current state of knowledge of stable homotopy groups of spheres. We describe a computational method using motivic homotopy theory, viewed as a deformation of classical homotopy theory. This yields a streamlined computation of the first 61 stable homotopy groups and gives information about the stable homotopy groups in dimensions 62 through 90. As an application, we determine the groups of homotopy spheres that classify smooth structures on spheres through dimension 90, except for dimension 4. The method relies more heavily on machine computations than previous methods and is therefore less prone to error. The main mathematical tool is the Adams spectral sequence.
  • 关键词:stable homotopy groups of spheres ; smooth structures on spheres ; Adams spectral sequence ; motivic homotopy theory
国家哲学社会科学文献中心版权所有