On the higher Whitehead groups of a Bieberbach group
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- by Andrew J. Nicas PDF
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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 Hsiangâs structure theorem for Bieberbach groups, parametrized surgery, pseudoisotopy, and Waldhausenâs algebraic $K$-theory of spaces.References
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Additional Information
- © Copyright 1985 American Mathematical Society
- 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