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

 

Relations among characteristic classes of $ n$-manifolds imbedded in $ {\bf R}\sp{n+k}$


Author: Stavros Papastavridis
Journal: Proc. Amer. Math. Soc. 79 (1980), 639-643
MSC: Primary 57R40; Secondary 57R20
MathSciNet review: 572319
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Abstract: Let $ {I_n} \subseteq {H^ \ast }(BO;{Z_2})$ be the (graded) set of those normal characteristic classes which are zero on all compact, closed $ {C^\infty }$ manifolds. Let $ {I_{n,k}} \subseteq {H^ \ast }(BO;{Z_2})$ be the set of those characteristic classes which are zero on all n-manifolds which imbed in $ {R^{n + k}}$. Let K be the (graded) ideal in $ {H^ \ast }(BO;{Z_2})$ generated by the Stiefel-Whitney classes $ {w_k},{w_{k + 1}},{w_{k + 2}},{w_{k + 3}}, \ldots $. We will prove the following result: If $ 1 \leqslant i \leqslant \min \{ (2k - 2),(n + k - 1)/2\} $, then $ I_{n,k}^i = I_n^i + {K^i}$ . Also, we will prove an analogous result for manifolds with an extra structure.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1980-0572319-2
PII: S 0002-9939(1980)0572319-2
Article copyright: © Copyright 1980 American Mathematical Society