The automorphism groups of spaces and fibrations

Sara Hurvitz

Vol. 96 (1981), No. 2, 371–388

DOI: 10.2140/pjm.1981.96.371

Abstract

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 → AutX_p) is isomorphic to Ker(AutY → AutY _p)(( )_p-localization of p).

Mathematical Subject Classification 2000

Primary: 55R05

Secondary: 55P10

Milestones

Received: 6 November 1979

Published: 1 October 1981