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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Relations among characteristic classes


Author: Stavros Papastavridis
Journal: Trans. Amer. Math. Soc. 237 (1978), 175-187
MSC: Primary 57D20
DOI: https://doi.org/10.1090/S0002-9947-1978-0470967-7
MathSciNet review: 0470967
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Abstract: Let M be an n-dimensional, compact, closed, $ {C^\infty }$ manifold, and $ v:M \to BO$ be the map classifying its stable normal bundle. Let $ S \subseteq {H^\ast}(BO;{Z_2})$ be a set of characteristic classes and let q, k, be fixed nonnegative integers. We define $ I_n^q(S,k) = \{ x \in {H^q}(B):{v^\ast}(x) \cdot y = 0$ for all $ y \in {H^k}(M;{Z_2})$ and for all n-dimensional, $ {C^\infty }$ closed compact manifolds M, which have the propery that $ {v^\ast}(S) = \{ 0\} \} $.

In this paper we compute $ I_n^q(S,k)$, where all classes of S have dimension greater than $ n/2$. We examine also the case of BSO and BU manifolds.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1978-0470967-7
Keywords: Characteristic classes, characteristic numbers, corbodism, surgery, Steenrod algebra, Serre spectral sequence
Article copyright: © Copyright 1978 American Mathematical Society

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