- Tytuł:
- Waldhausen’s Nil groups and continuously controlled K-theory
- Autorzy:
-
Munkholm, Hans
Prassidis, Stratos - Powiązania:
- https://bibliotekanauki.pl/articles/1205232.pdf
- Data publikacji:
- 1999
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Opis:
- 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 $BΓ_1 ← BG ← BΓ_2$. Denote by ξ the diagram $I {p \over ←} H {1 \over →} X = H$, where p is the natural map onto the unit interval. We show that the $Nil^∼$ groups which occur in Waldhausen's description of $K_*(ℤΓ)$ coincide with the continuously controlled groups $\widetildeK^{cc}_*(ξ)$, defined by Anderson and Munkholm. This also allows us to identify the continuously controlled groups $\widetildeK^{cc}_*(ξ^+)$ which are known to form a homology theory in the variable ξ, with the "homology part" in Waldhausen's description of $K_{*-1}(ℤ Γ)$. A similar result is also obtained for HNN extensions.
- Źródło:
-
Fundamenta Mathematicae; 1999, 161, 1-2; 217-224
0016-2736 - Pojawia się w:
- Fundamenta Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł