A counterexample to Wall's finite D(2) problem

What OpenAI claims

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.

Paper

1. A Counterexample to Wall's D(2) Problem

   6 October 2026 · Preprint, not peer reviewed · PDF

   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.

Status

Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.