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Transactions of the American Mathematical Society

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

 

 

On the higher Whitehead groups of a Bieberbach group


Author: Andrew J. Nicas
Journal: Trans. Amer. Math. Soc. 287 (1985), 853-859
MSC: Primary 18F25; Secondary 19D35, 19M05, 20F38, 57N37, 57R65
DOI: https://doi.org/10.1090/S0002-9947-1985-0768746-X
MathSciNet review: 768746
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Abstract: Let $ \Gamma $ be a Bieberbach group, i.e. the fundamental group of a compact flat Riemannian manifold. In this paper we show that if $ p > 2$ is a prime, then the $ p$-torsion subgroup of $ {\text{Wh}_i}(\Gamma )$ vanishes for $ 0 \leq i \leq 2p - 2$, where $ {\text{Wh}_i}(\Gamma )$ is the $ i$th higher Whitehead group of $ \Gamma $. The proof involves Farrell and Hsiang's structure theorem for Bieberbach groups, parametrized surgery, pseudoisotopy, and Waldhausen's algebraic $ K$-theory of spaces.


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DOI: https://doi.org/10.1090/S0002-9947-1985-0768746-X
Article copyright: © Copyright 1985 American Mathematical Society