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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Simple homotopy types for $ (G,\,m)$-complexes


Author: Micheal N. Dyer
Journal: Proc. Amer. Math. Soc. 81 (1981), 111-115
MSC: Primary 57Q10; Secondary 55P15
MathSciNet review: 589149
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Abstract: Let $ G$ be a finite group. We use the fact that each element of the Whitehead group Wh$ (G)$ may be represented by at most a $ 2 \times 2$ (nonsingular) matrix to deduce results about when simple homotopy type and homotopy type agree. As examples, we give complete descriptions of the simple homotopy types for $ ({Z_m} \times {Z_n},2)$-complexes, provided $ S{K_1}(Z({Z_m} \times {Z_n})) = 0$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1981-0589149-9
PII: S 0002-9939(1981)0589149-9
Article copyright: © Copyright 1981 American Mathematical Society