The Kahn-Priddy Theorem and the homotopy of the three-sphere

Authors:
Piotr Beben and Stephen Theriault

Journal:
Proc. Amer. Math. Soc. **141** (2013), 711-723

MSC (2010):
Primary 55P35, 55Q40

DOI:
https://doi.org/10.1090/S0002-9939-2012-11337-1

Published electronically:
June 12, 2012

MathSciNet review:
2996976

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Abstract: Let be an odd prime. The least nontrivial -torsion homotopy group of occurs in dimension and is of order . This induces a map , where is a mod- Moore space. An important conjecture related to the Kahn-Priddy Theorem is that the double loops on the three-connected cover of has a right homotopy inverse. We prove a weaker but still useful property: if is the cofiber of , then the double loop on the three-connected cover of the inclusion is null homotopic.

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Additional Information

**Piotr Beben**

Affiliation:
Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China

Email:
bebenp@unbc.ca

**Stephen Theriault**

Affiliation:
Department of Mathematical Sciences, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom

Email:
s.theriault@abdn.ac.uk

DOI:
https://doi.org/10.1090/S0002-9939-2012-11337-1

Keywords:
Three-sphere,
homotopy group

Received by editor(s):
July 1, 2011

Published electronically:
June 12, 2012

Communicated by:
Brooke Shipley

Article copyright:
© Copyright 2012
American Mathematical Society