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Algebraic classification of equivariant homotopy 2-types, I

Ieke Moerdijk ; Jan Alve Svensson (Institutionen för matematik, Matematik/Tillämpad matematik)
Journal of Pure and Applied Algebra (0022-4049). Vol. 89 (1993), 1-2, p. 187–216.
[Artikel, refereegranskad vetenskaplig]

We show that the category of diagrams of 2-groupoids indexed by the orbit category View the MathML source(G) of a group G admits a closed Quillen model structure. The associated homotopy category is then proved to be equivalent to the homotopy category of all G-spaces with the property that the nth homotopy group of each fixpoint set vanishes for n⩾3. This result is the equivariant analogue of the classical Mac Lane-Whitehead correspondence between crossed modules and pointed connected CW-complexes (X, x0) for which πi(X, x0)=0 for i⩾3.



Denna post skapades 2014-01-26.
CPL Pubid: 193079

 

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Institutioner (Chalmers)

Institutionen för matematik, Matematik/Tillämpad matematik (1987-2001)

Ämnesområden

Algebra och geometri

Chalmers infrastruktur