A candidate for a solution to Wall's D(2) problem

TL;DR

This paper discusses potential solutions to Wall's D(2) problem, the Realization problem, and the Relation Gap problem, linking them to the deficiency of certain groups, but it has been withdrawn.

Contribution

It proposes that proving the deficiency of specific groups is less than -1 could resolve major open problems in topology and group theory.

Findings

Presented a group with deficiency -1 in a related work

Connected group deficiency to topological problems

Discussed implications for the D(2) problem

Abstract

We show that Wall's D(2) problem, the Realization problem and the Relation Gap problem could all be solved if it could be shown that the deficiency of a certain group is, as intuition would suggest, less than -1. Note the paper has been withdrawn. A presentation of *_p (C_p x C_p)with deficiency -1 is given on p35 of: Cynthia Hog-Angeloni, Beitrage zum (einfachen) homotopietyp zweidimensionaler komplexe zu freein produkten und anderen gruppentheoretischen konstruktionen : PhD thesis, Frankfurt/Main 1988