A torus theorem for homotopy nilpotent loop spaces

Cristina Costoya Universidade da Coruña Jérôme Scherer École polytechnique fédérale de Lausanne (EPFL) Antonio Viruel Universidad de Málaga

Algebraic Topology and General Topology mathscidoc:1912.43005

Arkiv for Matematik, 56, (1), 53-71, 2018
Nilpotency for discrete groups can be defined in terms of central extensions. In this paper, the analogous definition for spaces is stated in terms of principal fibrations having infinite loop spaces as fibers, yielding a new invariant between the classical LS cocategory and the more recent notion of homotopy nilpotency introduced by Biedermann and Dwyer. This allows us to characterize finite homotopy nilpotent loop spaces in the spirit of Hubbuck’s Torus Theorem, and obtain corresponding results for p-compact groups and p-Noetherian groups.
nilpotent, homotopy nilpotent, cocategory, algebraic theory, Goodwillie calculus, excisive functor, p-compact group
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  title={A torus theorem for homotopy nilpotent loop spaces},
  author={Cristina Costoya, Jérôme Scherer, and Antonio Viruel},
  booktitle={Arkiv for Matematik},
Cristina Costoya, Jérôme Scherer, and Antonio Viruel. A torus theorem for homotopy nilpotent loop spaces. 2018. Vol. 56. In Arkiv for Matematik. pp.53-71. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191204092915583148561.
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