The algebraic EHP sequence

Singer, William M.

doi:10.1090/S0002-9947-1975-0385861-7

The algebraic EHP sequence
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by William M. Singer PDF

Trans. Amer. Math. Soc. 201 (1975), 367-382 Request permission

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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