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Proceedings of the American Mathematical Society

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

 

 

Killing characteristic classes by surgery


Author: Stavros Papastavridis
Journal: Proc. Amer. Math. Soc. 63 (1977), 353-358
MSC: Primary 57D20
DOI: https://doi.org/10.1090/S0002-9939-1977-0440568-X
MathSciNet review: 0440568
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Abstract: Let M be an n-dimensional $ {C^\infty }$ manifold and let

$\displaystyle c \in {H^\ast}(BO;{Z_2})$

be a characteristic class. Suppose that c as a factor annihilates all the characteristic numbers of M. We prove that if $ \dim c \geqslant (n + 1)/2$ then M is cobordant to a manifold which has the class c zero, in that way answering in the affirmative a question raised by C. T. C. Wall. We examine the same question for more general cobordism theories, and for $ {Z_p}$ characteristic classes.

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DOI: https://doi.org/10.1090/S0002-9939-1977-0440568-X
Keywords: Characteristic classes, characteristic numbers, cobordism, surgery, Steenrod Algebra, Serre spectral sequence
Article copyright: © Copyright 1977 American Mathematical Society