Equivariant CW-complexes and the orbit category

Equivariant CW-complexes and the orbit category

We give a general framework for studying $G$-CW complexes via the orbit category. As an application we show that the symmetric group $G=S_5$ admits a finite $G$-CW complex $X$ homotopy equivalent to a sphere, with cyclic isotropy subgroups.

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Veröffentlicht in:Commentarii mathematici Helvetici 2013-01, Vol.88 (2), p.369-425
Hauptverfasser: Hambleton, Ian, Pamuk, Semra, Yalçın, Ergün
Format: Artikel
Sprache:eng
Schlagworte:
Algebraic topology
Category theory
Group theory and generalizations
homological algebra
Manifolds and cell complexes
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Beschreibung
Zusammenfassung:We give a general framework for studying $G$-CW complexes via the orbit category. As an application we show that the symmetric group $G=S_5$ admits a finite $G$-CW complex $X$ homotopy equivalent to a sphere, with cyclic isotropy subgroups.
ISSN:0010-2571
1420-8946
DOI:10.4171/CMH/289