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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Generators of $ H\sp{\ast} (M{\rm SO};Z\sb{2})$ as a module over the Steenrod algebra, and the oriented cobordism ring


Author: Stavros Papastavridis
Journal: Proc. Amer. Math. Soc. 84 (1982), 285-290
MSC: Primary 55R40; Secondary 55S10, 57R75
MathSciNet review: 637185
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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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DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0637185-7
PII: S 0002-9939(1982)0637185-7
Keywords: Oriented cobordism, cohomology of MSO
Article copyright: © Copyright 1982 American Mathematical Society