Volume 14, issue 1 (2010)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
An elementary construction of Anick's fibration

Brayton Gray and Stephen Theriault

Geometry & Topology 14 (2010) 243–275

Erratum: Geometry & Topology 17 (2013) 2595–2600

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 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 T2n1 and use this to construct a secondary EHP 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
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