The Rational Homotopy Type of Homotopy Fibrations Over Connected Sums

TL;DR

This paper establishes a simple cohomological condition under which the rational homotopy type of a total space in a pullback fibration over a connected sum simplifies after looping, extending previous work with weaker assumptions.

Contribution

It introduces a new, less restrictive condition on rational cohomology that determines when the total space's rational homotopy type simplifies after looping in such fibrations.

Findings

Provides a criterion for the rational homotopy type of total spaces in pullback fibrations

Extends previous results by Jeffrey and Selick with weaker hypotheses

Shows the rational homotopy type simplifies to a connected sum after looping

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.