TY - JOUR
T1 - Automorphisms of fibrations
AU - Dror, E.
AU - Dwyer, W. G.
AU - Kan, D. M.
PY - 1980/11
Y1 - 1980/11
N2 - Let X be a simplicial set, G a simplicial group and WG the classifying complex of G. Then it is well known [1], [3] that the principal fibrations with base X and group G are classified by the components of the function complex (WG)X. The aim of the present note is to prove the following complement to this result (1.2): Let p be a principal fibration with base X and group G, and let aut p be its simplicial group of automorphisms (which keep the base fixed). Then W(aut p) has the homotopy type of the component of (WG)X which (see above) corresponds to p. A similar result holds for ordinary fibrations.
AB - Let X be a simplicial set, G a simplicial group and WG the classifying complex of G. Then it is well known [1], [3] that the principal fibrations with base X and group G are classified by the components of the function complex (WG)X. The aim of the present note is to prove the following complement to this result (1.2): Let p be a principal fibration with base X and group G, and let aut p be its simplicial group of automorphisms (which keep the base fixed). Then W(aut p) has the homotopy type of the component of (WG)X which (see above) corresponds to p. A similar result holds for ordinary fibrations.
UR - https://www.scopus.com/pages/publications/84966254989
U2 - 10.1090/S0002-9939-1980-0581012-1
DO - 10.1090/S0002-9939-1980-0581012-1
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AN - SCOPUS:84966254989
SN - 0002-9939
VL - 80
SP - 491
EP - 494
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 3
ER -