Killing characteristic classes by surgery

Papastavridis, Stavros

doi:10.1090/S0002-9939-1977-0440568-X

Killing characteristic classes by surgery
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Proc. Amer. Math. Soc. 63 (1977), 353-358 Request permission

Abstract:

Let M be an n-dimensional ${C^\infty }$ manifold and let \[ c \in {H^\ast }(BO;{Z_2})\] 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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