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Let be the pushout of two groups , i = 1,2, over a common subgroup G, and H be the double mapping cylinder of the corresponding diagram of classifying spaces . Denote by ξ the diagram , where p is the natural map onto the unit interval. We show that the groups which occur in Waldhausen’s description of coincide with the continuously controlled groups , defined by Anderson and Munkholm. This also allows us to identify the continuously controlled groups which are known to form a homology...
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