Geometry & Topology

An elementary construction of Anick's fibration

Brayton Gray and Stephen Theriault

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Cohen, Moore, and Neisendorfer’s work on the odd primary homotopy theory of spheres and Moore spaces, as well as the first author’s work on the secondary suspension, predicted the existence of a p–local fibration S2n1T2n1ΩS2n+1 whose connecting map is degree pr. In a long and complex monograph, Anick constructed such a fibration for p5 and r1. Using new methods we give a much more conceptual construction which is also valid for p=3 and r1. We go on to establish an H space structure on T2n1 and use this to construct a secondary EHP sequence for the Moore space spectrum.

Article information

Geom. Topol., Volume 14, Number 1 (2010), 243-275.

Received: 18 December 2007
Revised: 3 August 2009
Accepted: 1 September 2009
First available in Project Euclid: 20 December 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55P45: $H$-spaces and duals 55P40: Suspensions 55P35: Loop spaces

Anick's fibration double suspension EHP sequence Moore space


Gray, Brayton; Theriault, Stephen. An elementary construction of Anick's fibration. Geom. Topol. 14 (2010), no. 1, 243--275. doi:10.2140/gt.2010.14.243.

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