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arXiv · 2604.22004

Branched Bending in Finite-Volume Hyperbolic Manifolds

Casandra D. Monroe
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Abstract

We define branched bending deformations as deformations supported on a piecewise totally geodesic complex of $(n-1)$-dimensional faces meeting along $(n-2)$-dimensional branching loci. These are a generalization of bending deformations, as introduced by Johnson and Millson. We give a lower bound on the dimension of the (infinitesimal) deformation space supported on a branched bending complex, and in doing so generalize a result of Bart and Scannell. We give equations describing these deformations in the setting of deforming to higher hyperbolic geometry and real projective geometry. As a special example of branched bending, we construct infinitesimal deformations supported on the link complement of the Borromean Rings (also known as the link $6^3_2$), recovering a special case of a theorem due to Menasco and Reid.

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Casandra D. Monroe. 2026-04-23. Branched Bending in Finite-Volume Hyperbolic Manifolds. https://arxiv.org/abs/2604.22004

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