Closed Geodesic Length Bounds of Hyperbolic Link Complements in Hyperbolic $3$-Manifolds

Buddha Dev Ghosh

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arXiv · 2303.08963

Closed Geodesic Length Bounds of Hyperbolic Link Complements in Hyperbolic $3$-Manifolds

Buddha Dev Ghosh

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Abstract

Let $M$ be a compact hyperbolic $3$-manifold with volume $V$. Let $L$ be a link such that $M\setminus L$ is hyperbolic. For any hyperbolic link $L$ in $M$, in this article, we establish an upper bound of the length of an $n^{th}$ shortest closed geodesic as a logarithmic function of $V$ in $M\setminus L$. Our works complement the work of Lakeland and Leininger \cite{Christopher} on the upper bound of systole length.

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Buddha Dev Ghosh. 2023-03-15. Closed Geodesic Length Bounds of Hyperbolic Link Complements in Hyperbolic $3$-Manifolds. https://arxiv.org/abs/2303.08963

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