Generators of 𝐻*(𝑀𝑆𝑂;𝑍₂) as a module over the Steenrod algebra, and the oriented cobordism ring

Papastavridis, Stavros

doi:10.1090/S0002-9939-1982-0637185-7

Generators of $H^{\ast } (M\textrm {SO};Z_{2})$ as a module over the Steenrod algebra, and the oriented cobordism ring
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Proc. Amer. Math. Soc. 84 (1982), 285-290 Request permission

Abstract:

In this paper we will describe a minimal set of $A$-generators of ${H^* }(MSO;{Z_2})$ (where $A$ is the $\bmod {\mathbf { - }}2$ Steenrod Algebra). The description is very much analogous to ${\text {R}}$. Thom’s description of generators for ${H^*}(MO;{Z_2})$ (see [7]). As a corollary, we give simple cohomological criteria for a manifold to be indecomposable in the oriented cobordism. Our proof relies on work of D. J. Pengelley (see [5]).$^{1}$

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