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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Imbeddings, immersions, and characteristic classes of differentiable manifolds


Author: Stavros Papastavridis
Journal: Proc. Amer. Math. Soc. 69 (1978), 177-180
MSC: Primary 57D20; Secondary 55G36, 55G40, 57D40
MathSciNet review: 0488078
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Abstract: Let $ I_n^i$ be the set of $ \bmod {\text{ - }}2$ characteristic classes which are of dimension i, and they are zero for all n-dimensional smooth manifolds. Let $ I_{n,k}^i$ be the set of i-dimensional $ \bmod {\text{ - }}2$ characteristic classes which are zero for all n-dimensional smooth manifolds which immerse in codimension k, (we are talking about normal characteristic classes). Let K be the (graded) ideal in $ {H^ \ast }(BO,{Z_2})$ generated by $ {w_{k + 1}},{w_{k + 2}}, \ldots $. Then if $ i \leqslant (n + k)/2$, we have $ I_{n,k}^i = I_n^i + {K^i}$. We have some related results for imbedded manifolds, and also for manifolds which immerse or imbed with an SO, U, SU, Spin, etc. structure on the normal bundle.


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DOI: https://doi.org/10.1090/S0002-9939-1978-0488078-9
Keywords: Immersions, imbeddings, characteristic classes
Article copyright: © Copyright 1978 American Mathematical Society