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arXiv · 2208.05076

Moduli spaces of polygons and deformations of polyhedra with boundary

Sasha Anan'in·Dmitrii Korshunov
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Abstract

We prove a conjecture of Ian Agol: all isometric realizations of a polyhedral surface with boundary sweep out an isotropic subset in the Kapovich-Millson moduli space of polygons isomorphic to the boundary. For a generic polyhedral disk we show that boundaries of its isometric realizations make up a Lagrangian subset. As an application of this result, we obtain a new solution to the problem of Richard Kenyon about spanning domes of piecewise linear curves comprised of unit intervals in R^3.

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Sasha Anan'in, Dmitrii Korshunov. 2022-08-09. Moduli spaces of polygons and deformations of polyhedra with boundary. https://arxiv.org/abs/2208.05076

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