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Transactions of the American Mathematical Society

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On vanishing of characteristic numbers
in Poincaré complexes

Author: Yanghyun Byun
Journal: Trans. Amer. Math. Soc. 348 (1996), 3085-3095
MSC (1991): Primary 57P10, 57N65
MathSciNet review: 1322949
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Abstract: Let $G_r(X)\subset \pi _r(X)$ be the evaluation subgroup as defined by Gottlieb. Assume the Hurewicz map $G_r(X)\rightarrow H_r(X; R)$ is non-trivial and $R$ is a field. We will prove: if $X$ is a Poincaré complex oriented in $R$-coefficient, all the characteristic numbers of $X$ in $R$-coefficient vanish. Similarly, if $R=Z_p$ and $X$ is a $Z_p$-Poincaré complex, then all the mod $p$ Wu numbers vanish. We will also show that the existence of a non-trivial derivation on $H^*(X; Z_p)$ with some suitable conditions implies vanishing of mod $p$ Wu numbers.

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Additional Information

Yanghyun Byun
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556-5683
Address at time of publication: Department of Mathematics, Hanyang University, Seoul, 133-791 Korea

Keywords: Characteristic numbers, evaluation subgroup, Hurewicz map.
Received by editor(s): November 14, 1994
Received by editor(s) in revised form: March 20, 1995
Article copyright: © Copyright 1996 American Mathematical Society

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