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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

The algebraic EHP sequence


Author: William M. Singer
Journal: Trans. Amer. Math. Soc. 201 (1975), 367-382
MSC: Primary 55H15; Secondary 18G15, 55E35
DOI: https://doi.org/10.1090/S0002-9947-1975-0385861-7
MathSciNet review: 0385861
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Abstract: Let $ A$ be the dual of the $ \bmod - 2$ Steenrod algebra. If $ M,N$, are graded unstable $ A$-comodules, one can define and compute the derived functors $ {\text{Coext} _A}(M,N)$ using unstable injective resolutions of $ N$. Bousfield and Curtis have shown that these unstable Coext groups can be fit into a long exact ``EHP sequence", an algebraic analogue of the EHP sequence of homotopy theory. Our object in the present paper is to study the relationship between the $ E,H$, and $ P$ homomorphisms and the composition pairing $ {\text{Coext} _A}(N,R) \otimes {\text{Coext} _A}(M,N) \to {\text{Coext} _A}(M,R)$. Among our results is a formula that measures the failure of the composition product to commute.


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DOI: https://doi.org/10.1090/S0002-9947-1975-0385861-7
Keywords: Cohomology of the Steenrod algebra, unstable Adams spectral sequence
Article copyright: © Copyright 1975 American Mathematical Society