An elementary construction of Anick’s fibration

Gray, Brayton; Theriault, Stephen

doi:10.2140/gt.2010.14.243

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An elementary construction of Anick's fibration

Brayton Gray and Stephen Theriault

Geometry & Topology 14 (2010) 243–275

DOI: 10.2140/gt.2010.14.243

Correction: 10.2140/gt.2013.17.2595

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 $S^{2 n - 1} \to T_{2 n - 1} \to Ω S^{2 n + 1}$ whose connecting map is degree $p^{r}$ . In a long and complex monograph, Anick constructed such a fibration for $p \geq 5$ and $r \geq 1$ . Using new methods we give a much more conceptual construction which is also valid for $p = 3$ and $r \geq 1$ . We go on to establish an $H$ space structure on $T_{2 n - 1}$ and use this to construct a secondary $E H P$ sequence for the Moore space spectrum.

Keywords

Anick's fibration, double suspension, EHP sequence, Moore space

Mathematical Subject Classification 2000

Primary: 55P45, 55P40, 55P35

References

Publication

Received: 18 December 2007

Revised: 3 August 2009

Accepted: 1 September 2009

Preview posted: 21 October 2009

Published: 2 January 2010

Proposed: Paul Goerss

Seconded: Bill Dwyer, Ralph Cohen

Correction: 18 September 2013

Authors

Brayton Gray
Department of Math, Stats and Comp Sci University of Illinois at Chicago 851 S Morgan Street Chicago, IL, 60607-7045 USA

Stephen Theriault
Department of Mathematical Sciences University of Aberdeen Aberdeen AB24 3UE United Kingdom

Volume 14, issue 1 (2010)