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Waldhausen’s Nil groups and continuously controlled K-theory

Hans Munkholm, Stratos Prassidis (1999)

Fundamenta Mathematicae

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

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