On the higher Whitehead groups of a Bieberbach group

Nicas, Andrew J.

doi:10.1090/S0002-9947-1985-0768746-X

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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
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 is a prime, then the -torsion subgroup of ${\text{Wh}_i}(\Gamma )$ vanishes for $0 \leq i \leq 2p - 2$ , where ${\text{Wh}_i}(\Gamma )$ is the 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 -theory of spaces.

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