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Three-Relator Universal Group, Four-Relator Adian–Rabin Family, and Unrecognizability of #2(S2×S2)\#^2(S^2\times S^2)

Primarily AI-generated textHuman understanding: some partsmath.GR — Group Theorymath.GT — Geometric Topology

Contributed by Qiuyu Ren ↗

Version 1 / Nov 05, 2026 / CC BY 4.0

Abstract

We construct a universal group with 2 generators and 3 relators, and an Adian–Rabin family with 2 generators and 4 relators whose nontrivial groups are universal. The resulting presentations show that the standard smooth manifold #n(S2×S2)\#^n(S^2\times S^2) is unrecognizable up to homeomorphism or diffeomorphism for every fixed n ≥ 2.

Provenance statement

The main theorems were produced by ChatGPT's agent "dot." The agent spent less than half a day to obtain the main algebraic statements of the paper. Section 10 and some writeup adjustment was done using GPT-6 Astra in Codex.

Formalizations

Tools used

OpenAI
dot
OpenAI
CodexVersion GPT-6 Astra

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Version history

  1. v1 · 25 pagesSubmitted by Qiuyu RenInitial depositCurrentNov 05, 2026