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A counterexample to Wall's finite D(2) problem
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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A Counterexample to Wall's D(2) Problem
Oct 6, 2026·wall-d2-counterexample.pdf
We give a negative answer to Wall's finite problem. We construct a finite connected three-dimensional CW complex satisfying the finiteness condition but not homotopy equivalent to any finite CW complex of dimension at most two. The example has infinite fundamental group.