Quillen's Plus Construction and the D(2) problem
Wajid Mannan
TL;DR
This paper demonstrates that finite connected 3-complexes with cohomological dimension 2 can be constructed using Quillen's plus construction, linking the D(2) problem to properties of perfect normal subgroups.
Contribution
It establishes a novel connection between the D(2) problem and the application of Quillen's plus construction to Cayley complexes.
Findings
Construction of 3-complexes via Quillen's plus construction
Reduction of the D(2) problem to perfect normal subgroup questions
Homotopy equivalence established for complexes with cohomological dimension 2
Abstract
Given a finite connected 3-complex with cohomological dimension 2, we show it may be constructed up to homotopy by applying the Quillen plus construction to the Cayley complex of a finite group presentation. This reduces the D(2) problem to a question about perfect normal subgroups.
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