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arXiv · 2603.25890

Nilpotent groups have polynomially bounded homological filling invariants

Gabriel Pallier
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Abstract

Gromov claimed, with a sketch of proof, that simply connected nilpotent Lie groups have polynomially bounded filling invariants. The literature establishes this, often with a stronger conclusion where the exponent of polynomiality is computed or estimated, for some classes of nilpotent groups, or ranges of filling degrees. We provide a proof, in part based on Gromov's hints, yielding at once (non-optimal) polynomial upper bounds on the homological filling invariants in every degree for all finitely generated nilpotent groups, or equivalently, for all simply connected nilpotent Lie groups having lattices.

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Gabriel Pallier. 2026-03-26. Nilpotent groups have polynomially bounded homological filling invariants. https://arxiv.org/abs/2603.25890

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