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Representation theory of homotopy types with at most two non-trivial homotopy groups localized at a prime
Published online by Cambridge University Press: 01 March 2000
Abstract
It is a classical result of Postnikov [15] that homotopy types X with at most two non-trivial homotopy groups πmX = A and πnX = B, 2 [les ] m < n, are classified by the k-invariant
formula here
Here the cohomology group of the Eilenberg–MacLane space K(A, m) was computed by Eilenberg–MacLane [11] and Cartan [5]. Let p be a prime and let ℤp ⊂ ℚ be the smallest subring of ℚ containing 1/q for all primes q with q ≠ p. We consider finitely generated ℤp-modules A and B and the stable range n < 2m − 1. Hence X is a p-local space with at most two non-trivial homotopy groups in a stable range. Then the homotopy type of X admits a product decomposition
formula here
where all Xi with 1 [les ] i [les ] j are indecomposable and this decomposition is unique up to permutation. We classify in this paper the indecomposable factors in (2) by the following result.
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- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 128 , Issue 2 , March 2000 , pp. 283 - 300
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- © The Cambridge Philosophical Society 2000
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