OpenAI research collection · 1 manuscript · Source checked 2026-10-19
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.
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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.
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