Year: 2026
Type: preprint
Abstract: In recent work, Stokes and Vermant considered graph-of-groups realisations of hypergraphs as a new description of rigidity-theoretic problems. In this paper, we show that the infinitesimal aspects of graph-of-groups realisations can be analysed using cellular sheaves and their cohomology. Using these tools, we give an algebraic condition for Henneberg moves to preserve independence, and we prove that the infinitesimal rigidity and flexibility of certain graph-of-groups realisations are generic properties. We use these results to show that whenever a rigidity-theoretic problem is defined in a Lie group $G$ using a $1$-dimensional connected subgroup $H$ with $N_{G}(H)/H$ finite, then the so-called Maxwell-count leads to a necessary and sufficient condition for minimal rigidity, generalising various known results in the literature.
Source: arXiv (Cornell University)
Author: Vermant, Joannes
Institution: Umeå University
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7134066384
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