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 a recent work of Jeffrey and Selick, in which they study pullback fibrations of this type but under stronger hypotheses compared to our result.

Homotopy of manifolds stabilized by projective spaces

“…To the best of our knowledge, the only surgery that has been studied from a homotopy theoretic point of view is a connected sum. In that case, there are numerous rational results, for example, [6, 11, 16], but integrally or $$p$$‐locally there are only a few very recent results in [20, Theorem 1.4], [4, 12].…”