Geometry & Topology

An elementary construction of Anick's fibration

Brayton Gray and Stephen Theriault

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513732176

Digital Object Identifier
doi:10.2140/gt.2010.14.243

Mathematical Reviews number (MathSciNet)
MR2578305

Zentralblatt MATH identifier
1185.55011

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

Keywords
Anick's fibration double suspension EHP sequence Moore space

Citation

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. https://projecteuclid.org/euclid.gt/1513732176


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