Branched Bending in Finite-Volume Hyperbolic Manifolds
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866913058259992576 |
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| author | Monroe, Casandra D. |
| author_facet | Monroe, Casandra D. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_22004 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Branched Bending in Finite-Volume Hyperbolic Manifolds Monroe, Casandra D. Geometric Topology Differential Geometry 57M50 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. |
| title | Branched Bending in Finite-Volume Hyperbolic Manifolds |
| topic | Geometric Topology Differential Geometry 57M50 |
| url | https://arxiv.org/abs/2604.22004 |