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$ v\sb 1$-periodic $ {\rm Ext}$ over the Steenrod algebra

Authors: Donald M. Davis and Mark Mahowald
Journal: Trans. Amer. Math. Soc. 309 (1988), 503-516
MSC: Primary 55T15; Secondary 55Q45, 55S10
MathSciNet review: 931531
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Abstract: For a large family of modules $ M$ over the $ \bmod 2$ Steenrod algebra $ A$, $ \operatorname{Ext} _A^{s,t}(M,\,{{\mathbf{Z}}_2})$ is periodic for $ t < 4s$ with respect to operators $ v_1^{2n}$ of period $ ({2^n},\,3 \cdot {2^n})$ for varying $ n$. $ v_1^{ - 1}\operatorname{Ext} _A^{s,t}(M,\,{{\mathbf{Z}}_2})$ can be defined by extending this periodic behavior outside this range. We calculate this completely when $ M = {H^{\ast}}(Y)$, where $ Y$ is the suspension spectrum of $ {\mathbf{R}}{P^2} \wedge {\mathbf{C}}{P^2}$.

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Keywords: Cohomology of Steenrod algebra, $ {v_1}$-periodicity, spectral sequences
Article copyright: © Copyright 1988 American Mathematical Society

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