# The Rational Sectional Category of Certain Universal Fibrations

## TL;DR

This paper proves that for a broad class of spaces satisfying Halperin's conjecture, the rationalized sectional category of their universal fibrations is exactly one, advancing understanding in algebraic topology.

## Contribution

It establishes that the sectional category of universal fibrations with certain spaces as fibers equals one after rationalization, confirming a specific case of a conjecture.

## Key findings

- Sectional category equals one after rationalization for these fibrations.
- Supports Halperin's conjecture in the context of universal fibrations.
- Advances the understanding of the structure of universal fibrations in rational homotopy theory.

## Abstract

We prove that the sectional category of the universal fibration with fibre X, for X any space that satisfies a well-known conjecture of Halperin, equals one after rationalization.