{"id":"openai-math/A-Counterexample-to-Walls-D2-Problem","pdf":"https://github.com/openai/math/blob/main/preprints/A-Counterexample-to-Walls-D2-Problem-October-6-2026/wall-d2-counterexample.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-Counterexample-to-Walls-D2-Problem-October-6-2026","tags":["homotopy-theory","cw-complexes","finiteness"],"score":0,"title":"A Counterexample to Wall's D(2) Problem","domain":"Topology","family":"321","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.GT","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-06","reactions":{},"formalized":false,"family_title":"A counterexample to Wall's finite D(2) problem"}