Variation of holonomy for projective structures and an application to drilling hyperbolic 3-manifolds

Martin Bridgeman; Kenneth Bromberg

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arXiv · 2310.10890

Variation of holonomy for projective structures and an application to drilling hyperbolic 3-manifolds

Martin Bridgeman·Kenneth Bromberg

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Abstract

We bound the derivative of complex length of a geodesic under variation of the projective structure on a closed surface in terms of the norm of the Schwarzian in a neighborhood of the geodesic. One application is to cone-manifold deformations of acylindrical hyperbolic 3-manifolds.

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Martin Bridgeman, Kenneth Bromberg. 2023-10-16. Variation of holonomy for projective structures and an application to drilling hyperbolic 3-manifolds. https://arxiv.org/abs/2310.10890

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