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Abelian Properties of Anick Spaces

About this Title

Brayton Gray, Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 S. Morgan Street, Chicago, Illinois 60607-7045

Publication: Memoirs of the American Mathematical Society
Publication Year: 2017; Volume 246, Number 1162
ISBNs: 978-1-4704-2308-7 (print); 978-1-4704-3633-9 (online)
Published electronically: September 29, 2016
MSC: Primary 55Q15, 55Q20, 55Q51; Secondary 55Q40, 55Q52, 55R99

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Table of Contents


  • 1. Introduction
  • 2. Abelian Structures
  • 3. Whitehead Products
  • 4. Index $p$ approximation
  • 5. Simplification
  • 6. Constructing $\gamma _k$
  • 7. Universal Properties
  • A. The Case $n=1$ and the Case $p=3$


Anick spaces are closely connected with both EHP sequences and the study of torsion exponents. In addition they refine the secondary suspension and enter unstable periodicity. In this work we describe their $H$-space properties as well as universal properties. Techniques include a new kind on Whitehead product defined for maps out of co-H spaces, calculations in an additive category that lies between the unstable category and the stable category, and a controlled version of the extension theorem of Gray and Theriault (Geom. Topol. 14 (2010), no. 1, 243–275).

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