A short elementary proof of Beben and Theriault's theorem on homotopy fibers

TL;DR

This paper provides a concise and elementary proof of a theorem by Beben and Theriault concerning the homotopy fiber of an extension of a map related to cone attachments, simplifying previous proofs.

Contribution

The paper introduces a shorter, more elementary proof of Beben and Theriault's theorem on homotopy fibers, making the result more accessible.

Findings

Simplified proof of Beben and Theriault's theorem

Enhanced understanding of homotopy fibers in cone attachments

Potential for broader applications due to elementary approach

Abstract

Beben and Theriault proved a theorem on the homotopy fiber of an extension of a map with respect to a cone attachment, which has produced several applications. We give a short and elementary proof of this theorem.