A simple homotopy-theoretical proof of the Sullivan conjecture

TL;DR

This paper presents a straightforward homotopy-theoretical proof of the Sullivan conjecture, demonstrating that the space of pointed maps from the classifying space of a cyclic group of order p to any finite-dimensional CW complex is contractible.

Contribution

It provides a simpler, homotopy-theoretical proof of the Sullivan conjecture, avoiding complex techniques used in previous proofs.

Findings

Confirmed the contractibility of the mapping space in the conjecture

Simplified the proof technique using homotopy theory

Validated the conjecture for finite-dimensional CW complexes

Abstract

We give a new proof, using comparatively simple techniques, of the Sullivan conjecture: the space of pointed maps from the classifying space of the cyclic group of order $p$ to any finite-dimensional CW complex $K$ is contractible.