Wall’s D2 problem

Groups, moves and rules · 1965

created November 2, 2026 · updated November 2, 2026

Wall’s 1965 question: if for a three-dimensional shape the third dimension adds nothing to the count of “holes” (such shapes are called D2 complexes), can it be deformed into a two-dimensional one. The paper arXiv 2610.23637 builds from the group “step and lift” a shape of six cells by attaching one solid cell: it does not reduce to a two-dimensional one. This conclusion is conditional: it rests on an OpenAI preprint of 6 October 2026, and there has been no independent check yet.

Source: arXiv 2610.23637: Corollary B and its dependence on the OpenAI preprint

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