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A Counterexample to Wall's D(2) Problem

OpenAI

OpenAI Mathopenai-math/A-Counterexample-to-Walls-D2-ProblemOct 6, 2026math.GTAI-generatedscore 0

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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