Coformality around fibrations and cofibrations

TL;DR

This paper investigates how coformality properties are transferred between base spaces, total spaces, and cofibers within fibrations, revealing new dualities and applications in algebraic topology.

Contribution

It establishes that coformality of the base implies coformality of the total space in fibrations under certain conditions, and explores dual results and applications.

Findings

Coformality of base implies coformality of total space in fibrations.

Coformality of cofiber implies coformality of base in certain cofibrations.

Total spaces of specific spherical fibrations are Koszul.

Abstract

We show that in a fibration the coformality of the base space implies the coformality of the total space under reasonable conditions, and these conditions can not be weakened. The result is partially dual to the classical work of Lupton \cite{Lup} on the formality within a fibration. Our result has two applications. First, we show that for certain cofibrations, the coformality of the cofiber implies the coformality of the base. Secondly, we show that the total spaces of certain spherical fibrations are Koszul in the sense of Berglund \cite{Ber}.