Work

Two-generator presentations with a relation gap

Year: 2026

Type: preprint

Abstract: We exhibit two-generator two-relator group presentations that have cyclic relation modules but do not present one-relator groups; this resolves the relation gap problem. By attaching a single 3-cell to each of the corresponding presentation 2-complexes, one obtains counterexamples to Wall's D2 problem.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.23637

Authors: Bartholdi, Laurent, Bridson, Martin R., Mikhailov, Roman, Nicholson, John

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung

Award: Automata, dynamics and actions

OpenAlex ID: W7222926988

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