## Geometry & Topology

### An elementary construction of Anick's fibration

#### 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 $S2n−1→T2n−1→ΩS2n+1$ whose connecting map is degree $pr$. In a long and complex monograph, Anick constructed such a fibration for $p≥5$ and $r≥1$. Using new methods we give a much more conceptual construction which is also valid for $p=3$ and $r≥1$. We go on to establish an $H$ space structure on $T2n−1$ 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
Revised: 3 August 2009
Accepted: 1 September 2009
First available in Project Euclid: 20 December 2017

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

#### 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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