Projective modules and the homotopy classification of (G,n)–complexes
Algebraic and Geometric Topology, Tome 24 (2024) no. 4, pp. 2245-2284
Voir la notice de l'article provenant de la source Mathematical Sciences Publishers
A (G,n)–complex is an n–dimensional CW–complex with fundamental group G and whose universal cover is (n−1)–connected. If G has periodic cohomology then, for appropriate n, we show that there is a one-to-one correspondence between the homotopy types of finite (G,n)–complexes and the orbits of the stable class of a certain projective ℤG–module under the action of Aut (G). We develop techniques to compute this action explicitly and use this to give an example where the action is nontrivial.
Keywords:
2–complexes, CW–complexes, $\mathbb{Z}G$–modules,
projective modules, finiteness obstruction
Affiliations des auteurs :
Nicholson, John 1
@article{10_2140_agt_2024_24_2245,
author = {Nicholson, John},
title = {Projective modules and the homotopy classification of {(G,n){\textendash}complexes}},
journal = {Algebraic and Geometric Topology},
pages = {2245--2284},
publisher = {mathdoc},
volume = {24},
number = {4},
year = {2024},
doi = {10.2140/agt.2024.24.2245},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.2245/}
}
TY - JOUR AU - Nicholson, John TI - Projective modules and the homotopy classification of (G,n)–complexes JO - Algebraic and Geometric Topology PY - 2024 SP - 2245 EP - 2284 VL - 24 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.2245/ DO - 10.2140/agt.2024.24.2245 ID - 10_2140_agt_2024_24_2245 ER -
%0 Journal Article %A Nicholson, John %T Projective modules and the homotopy classification of (G,n)–complexes %J Algebraic and Geometric Topology %D 2024 %P 2245-2284 %V 24 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.2245/ %R 10.2140/agt.2024.24.2245 %F 10_2140_agt_2024_24_2245
Nicholson, John. Projective modules and the homotopy classification of (G,n)–complexes. Algebraic and Geometric Topology, Tome 24 (2024) no. 4, pp. 2245-2284. doi: 10.2140/agt.2024.24.2245
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