Moduli spaces of polygons and deformations of polyhedra with boundary
Symplectic Geometry
2022-08-11 v1 Combinatorics
Metric Geometry
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.
Keywords
Cite
@article{arxiv.2208.05076,
title = {Moduli spaces of polygons and deformations of polyhedra with boundary},
author = {Sasha Anan'in and Dmitrii Korshunov},
journal= {arXiv preprint arXiv:2208.05076},
year = {2022}
}
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