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- W4299560007 abstract "An unknotting tunnel in a 3-manifold with boundary is a properly embedded arc, the complement of an open neighborhood of which is a handlebody. A geodesic with endpoints on the cusp boundary of a hyperbolic 3-manifold and perpendicular to the cusp boundary is called a vertical geodesic. Given a vertical geodesic in a hyperbolic 3-manifold M, we find sufficient conditions for it to be an unknotting tunnel. In particular, if the vertical geodesic corresponds to a 4-bracelet, 5-bracelet or 6-bracelet in the universal cover and has short enough length, it must be an unknotting tunnel. Furthermore, we consider a vertical geodesic that satisfies the elder sibling property, which means that in the universal cover, every horoball except the one centered at infinity is connected to a larger horoball by a lift of the vertical geodesic. Such a vertical geodesic with length less than ln(2) is then shown to be an unknotting tunnel." @default.
- W4299560007 created "2022-10-02" @default.
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- W4299560007 creator A5051801957 @default.
- W4299560007 date "2012-05-23" @default.
- W4299560007 modified "2023-09-27" @default.
- W4299560007 title "Unknotting tunnels in hyperbolic 3-manifolds" @default.
- W4299560007 doi "https://doi.org/10.48550/arxiv.1205.5239" @default.
- W4299560007 hasPublicationYear "2012" @default.
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