Relations among characteristic classes of 𝑛-manifolds imbedded in 𝑅^{𝑛+𝑘}

Papastavridis, Stavros

doi:10.1090/S0002-9939-1980-0572319-2

Relations among characteristic classes of $n$-manifolds imbedded in $\textbf {R}^{n+k}$
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by Stavros Papastavridis

Proc. Amer. Math. Soc. 79 (1980), 639-643

DOI: https://doi.org/10.1090/S0002-9939-1980-0572319-2

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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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