# Quasirationality and aspherical (pro-$p$)presentations

## TL;DR

This paper investigates quasirational (pro-$p$) presentations, exploring their properties and differences from aspherical presentations, and discusses implications for Whitehead's conjecture, confirming the existence of a broad class of such presentations.

## Contribution

It introduces and analyzes quasirational (pro-$p$) presentations, highlighting their distinctions from aspherical presentations and confirming the existence of a large class of these presentations.

## Key findings

- Quasirational (pro-$p$) presentations are distinct from aspherical presentations.
- The study sheds light on Whitehead's conjecture.
- Confirms the existence of a proper class of quasirational presentations.

## Abstract

Quasirational (pro-$p$)presentations are studied. The difference between aspherical and quasirational presentations sheds some light on the Whitehead's conjecture. We confirm expectations O.V. Melnikov on existence of a proper class of presentations.