Geodesic
Waldhausen’s Nil groups and continuously controlled K-theory
Fundamenta Mathematicae, Tome 161 (1999) no. 1, pp. 217-224 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

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.
DOI : 10.4064/fm-161-1-2-217-224

Hans J. Munkholm 1 ; Stratos Prassidis 1

1 
@article{10_4064_fm_161_1_2_217_224,
     author = {Hans J. Munkholm and Stratos Prassidis},
     title = {Waldhausen{\textquoteright}s {Nil} groups and continuously controlled {K-theory}},
     journal = {Fundamenta Mathematicae},
     pages = {217--224},
     year = {1999},
     volume = {161},
     number = {1},
     doi = {10.4064/fm-161-1-2-217-224},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/fm-161-1-2-217-224/}
}
TY  - JOUR
AU  - Hans J. Munkholm
AU  - Stratos Prassidis
TI  - Waldhausen’s Nil groups and continuously controlled K-theory
JO  - Fundamenta Mathematicae
PY  - 1999
SP  - 217
EP  - 224
VL  - 161
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4064/fm-161-1-2-217-224/
DO  - 10.4064/fm-161-1-2-217-224
LA  - en
ID  - 10_4064_fm_161_1_2_217_224
ER  - 
%0 Journal Article
%A Hans J. Munkholm
%A Stratos Prassidis
%T Waldhausen’s Nil groups and continuously controlled K-theory
%J Fundamenta Mathematicae
%D 1999
%P 217-224
%V 161
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4064/fm-161-1-2-217-224/
%R 10.4064/fm-161-1-2-217-224
%G en
%F 10_4064_fm_161_1_2_217_224
Hans J. Munkholm; Stratos Prassidis. Waldhausen’s Nil groups and continuously controlled K-theory. Fundamenta Mathematicae, Tome 161 (1999) no. 1, pp. 217-224. doi: 10.4064/fm-161-1-2-217-224

Cité par Sources :