Ext over the subalgebra \(A_ 2\) of the Steenrod algebra for stunted projective spaces. (English) Zbl 0568.55023
Current trends in algebraic topology, Semin. London/Ont. 181, CMS Conf. Proc. 2, 1, 297-342 (1982).
[For the entire collection see Zbl 0538.00016.]
Let \(A_ n\) denote the subalgebra of the mod two Steenrod algebra A generated by \(Sq^ 1,...,Sq^{2^ n}\) and let \(P_ n=H^*(RP/RP^{n-1};{\mathbb{Z}}_ 2)\). The authors use Koszul resolutions to calculate \(Ext_{A_ 2}(P_ n,{\mathbb{Z}}_ 2)\) for all n. They also begin a program of applying this computation to the study of immersions of projective spaces. The difficulty in this approach is that \(A//A_ 2\) is not realizable as the cohomology of a spectrum although it is a direct summand of the A-module \(H^*(MO<8>\);\({\mathbb{Z}}_ 2)\). An application to the computation of root invariants is also given.
Let \(A_ n\) denote the subalgebra of the mod two Steenrod algebra A generated by \(Sq^ 1,...,Sq^{2^ n}\) and let \(P_ n=H^*(RP/RP^{n-1};{\mathbb{Z}}_ 2)\). The authors use Koszul resolutions to calculate \(Ext_{A_ 2}(P_ n,{\mathbb{Z}}_ 2)\) for all n. They also begin a program of applying this computation to the study of immersions of projective spaces. The difficulty in this approach is that \(A//A_ 2\) is not realizable as the cohomology of a spectrum although it is a direct summand of the A-module \(H^*(MO<8>\);\({\mathbb{Z}}_ 2)\). An application to the computation of root invariants is also given.
Reviewer: S.Kochman
MSC:
| 55T15 | Adams spectral sequences |
| 55S40 | Sectioning fiber spaces and bundles in algebraic topology |
| 57R42 | Immersions in differential topology |
| 18G15 | Ext and Tor, generalizations, Künneth formula (category-theoretic aspects) |
