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

• DOI: 10.48550/arxiv.0811.4628
• Publication Date: 2008-01-01
• Authors: Mannan, W. H.
• Keywords: 20F05; 57M20; 57M20; 20F05; FOS: Mathematics; Group Theory (math.GR); 0101 mathematics; Mathematics - Group Theory; 01 natural sciences

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 Note the paper has been withdrawn.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<br/>This paper has been withdrawn by W.H.Mannan as the results are vacuous in light of the following: Def(*_p (C_p x C_p)) = -1, where the free product is taken over distinct primes p<br/>