The Rational Homotopy Type of Homotopy Fibrations Over Connected Sums

Abstract

We provide a simple condition on rational cohomology for the total space of a pullback fibration over a connected sum to have the rational homotopy type of a connected sum, after looping. This takes inspiration from recent work of Jeffrey and Selick, in which they study pullback fibrations of this type, but under stronger hypotheses compared to our result.

This version published by Proceedings of the Edinburgh Mathematical Society on 3rd April 2023