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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Equivariant maps which are self homotopy equivalences


Authors: E. Dror, W. G. Dwyer and D. M. Kan
Journal: Proc. Amer. Math. Soc. 80 (1980), 670-672
MSC: Primary 55P15
DOI: https://doi.org/10.1090/S0002-9939-1980-0587952-1
MathSciNet review: 587952
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Abstract: The aim of this note is (i) to give (in §2) a precise statement and proof of the (to some extent well-known) fact that the most elementary homotopy theory of ``simplicial sets on which a fixed simplicial group H acts'' is equivalent to the homotopy theory of ``simplicial sets over the classifying complex $ \bar WH$", and (ii) to use this (in §1) to prove a classification theorem for simplicial sets with an H-action, which provides classifying complexes for their equivariant maps which are self homotopy equivalences.


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DOI: https://doi.org/10.1090/S0002-9939-1980-0587952-1
Article copyright: © Copyright 1980 American Mathematical Society