$v_ 1$-periodic $\textrm {Ext}$ over the Steenrod algebra
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- by Donald M. Davis and Mark Mahowald PDF
- Trans. Amer. Math. Soc. 309 (1988), 503-516 Request permission
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 ${\mathbf {R}}{P^2} \wedge {\mathbf {C}}{P^2}$.References
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Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 309 (1988), 503-516
- MSC: Primary 55T15; Secondary 55Q45, 55S10
- DOI: https://doi.org/10.1090/S0002-9947-1988-0931531-2
- MathSciNet review: 931531