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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Odd primary $bo$ resolutions
and classification of the stable summands
of stunted lens spaces

Author: Jesús González
Journal: Trans. Amer. Math. Soc. 352 (2000), 1149-1169
MSC (1991): Primary 55P15; Secondary 55N20, 55P42, 55Q50, 55T15.
Published electronically: March 10, 1999
MathSciNet review: 1491866
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Abstract: The classification of the stable homotopy types of stunted lens spaces and their stable summands can be obtained by proving the triviality of certain stable classes in the homotopy groups of these spaces. This is achieved in the 2-primary case by Davis and Mahowald using classical Adams spectral sequence techniques. We obtain the odd primary analogue using the corresponding Adams spectral sequence based at the spectrum representing odd primary connective $K$-theory. The methods allow us to answer a stronger problem: the determination of the smallest stunted space where such stable classes remain null homotopic. A technical problem prevents us from giving an answer in all situations; however, in a quantitative way, the number of cases missed is very small.

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Additional Information

Jesús González
Affiliation: Departamento de Matemáticas, Cinvestav, AP 14-740, México DF 07000

PII: S 0002-9947(99)02284-9
Received by editor(s): November 18, 1994
Received by editor(s) in revised form: August 1, 1997
Published electronically: March 10, 1999
Article copyright: © Copyright 1999 American Mathematical Society

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