Vol. 96, No. 2, 1981

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The automorphism groups of spaces and fibrations

Sara Hurvitz

Vol. 96 (1981), No. 2, 371–388

This paper deals with the automorphism group of fibrations f : X Y , where X and Y are simply connected CW-complexes with either a finite number of homology groups or homotopy groups. It is proved that the automorphism groups of such fibrations are finitely presented, and that in case X and Y are H0-spaces the image of the obvious map Aut(f) Aut(H(f,Z)) has finite index in Aut(H(f,Z)). It is also proved that in case that Y belongs to the genus of X, Ker(AutX AutXp) is isomorphic to Ker(AutY AutY p)(( )p-localization of p).

Mathematical Subject Classification 2000
Primary: 55R05
Secondary: 55P10
Received: 6 November 1979
Published: 1 October 1981
Sara Hurvitz