The homology of \(\operatorname{MSpin}\). (English) Zbl 0554.55003
Let \(A\) denote the mod 2 Steenrod algebra, and let \(A_1\) be the dual of the subalgebra of \(A\) generated by \(Sq^1\) and \(Sq^2\). The authors determine the structure of \(H_*(\operatorname{MSpin};\mathbb{Z}/2)\) as an \(A\)-comodule algebra. The simultaneous determination of these two structures leads, via the Adams spectral sequence, to interesting new information on the product structure of the bordism ring \(\Omega_*^{\operatorname{Spin}}\) extending the result of D. W. Anderson, E. H. Brown jun. and F. P. Petersen [Ann. Math. (2) 89, 271–298 (1967; Zbl 0156.21605)]. The authors’ method is to use the identification of \(H_*(\operatorname{MSpin};\mathbb{Z}/2)\) with \(A\square_{A_1}N\) [the second author, Proc. Am. Math. Soc. 87, 355–356 (1983; Zbl 0517.55012)]. The bulk of this paper is devoted to the analysis of the structure of \(N\).
Reviewer: S. O. Kochmann
MSC:
| 55N22 | Bordism and cobordism theories and formal group laws in algebraic topology |
| 55T15 | Adams spectral sequences |
| 57R90 | Other types of cobordism |
| 55S10 | Steenrod algebra |
| 55P42 | Stable homotopy theory, spectra |
References:
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| [7] | DOI: 10.1112/jlms/s2-25.3.467 · Zbl 0458.55003 · doi:10.1112/jlms/s2-25.3.467 |
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