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Nilpotent groups with Dehn function $n^2 \log n$

Year: 2026

Type: preprint

Abstract: We exhibit 2-step Carnot groups with Dehn function $n^2 \log n$, sharpening Wenger's superquadratic lower bound for these groups. Some of these groups admit lattices, yielding finitely generated nilpotent groups with Dehn function $n^2 \log n$. This gives the first exact computation of a Dehn function which does not grow like $n^α$ for any $α\geq 1$ among nilpotent groups and, more generally, among finitely presented solvable groups with subexponential Dehn function.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2608.23702

Author: Vandermeersch, Ken

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Vlaamse regering

Award: Classification, symmetries and singularities at the frontiers of algebra, analysis and geometry.

OpenAlex ID: W7204230663

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