Automorphisms of fibrations
Copyright policy )Automorphisms of fibrations
Let X be a simplicial set, G a simplicial group and W ¯ G \bar 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 ( W ¯ G ) X {(\bar 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 ) \bar W({\operatorname {aut}}\,p) has the homotopy type of the component of ( W ¯ G ) X {(\bar WG)^X} which (see above) corresponds to p. A similar result holds for ordinary fibrations.
- Hebrew University of Jerusalem Israel
- Massachusetts Institute of Technology United States
- Yale University United States
Simplicial sets and complexes in algebraic topology, Fiber spaces in algebraic topology, classifying space of the simplicial group of automorphisms of a fibration, simplicial localization, principal fibration, Homotopy equivalences in algebraic topology, minimal fibration, Classifying spaces of groups and \(H\)-spaces in algebraic topology
Simplicial sets and complexes in algebraic topology, Fiber spaces in algebraic topology, classifying space of the simplicial group of automorphisms of a fibration, simplicial localization, principal fibration, Homotopy equivalences in algebraic topology, minimal fibration, Classifying spaces of groups and \(H\)-spaces in algebraic topology
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