Rational fibrations, minimal models, and fibrings of homogeneous spaces

Abstract

Sullivan’s theory of minimal models is used to study a class of maps called rational fibrations, which contains most Serre fibrations. It is shown that if the total space has finite rank and the fibre has finite dimensional cohomology, then both fibre and base have finite rank. This is applied to prove that certain homogeneous spaces cannot be the total space of locally trivial bundles. In addition two main theorems are proved which exhibit a close relation between the connecting homomorphism of the long exact homotopy sequence, and certain properties of the cohomology of fibre and base.