Constructs a finite connected three-dimensional CW complex whose universal cover has no integral homology above degree two and whose third cohomology vanishes for every local coefficient module, but which has no finite two-dimensional homotopy model. This disproves Wall's finite D(2) conjecture; the example has infinite fundamental group.
Manuscript
A Counterexample to Wall's D(2) Problem
October 6, 2026 · source · cite as \cite{OAI:A-Counterexample-to-Walls-D2-Problem-October-6-2026}
We give a negative answer to Wall's finite D(2) problem. We construct a finite connected three-dimensional CW complex satisfying the D(2) finiteness condition but not homotopy equivalent to any finite CW complex of dimension at most two. The example has infinite fundamental group.
Result 321 · Topology. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.
Source: https://github.com/openai/math/blob/main/CONTENTS.md