Unknotting tunnels in two-bridge knot and link complements |
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Authors: | Colin C Adams Alan W Reid |
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Institution: | (1) Department of Mathematics, Williams College, 01267 Williamstown, MA, USA;(2) Department of Mathematics, University of Texas, 78712 Austin, TX, USA |
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Abstract: | We give a complete classification of the unknotting tunnels in 2-bridge link complements, proving that only the upper and
lower tunnels are unknotting tunnels. Moreover, we show that the only strongly parabolic tunnels in 2-cusped hyperbolic 3-manifolds
are exactly the upper and lower tunnels in 2-bridge knot and link complements. From this, it follows that the upper and lower
tunnels in 2-bridge knot and link complements must be isotopic to geodesics of length at most ln(4), where length is measured
relative to maximal cusps. Moreover, the four dual unknotting tunnels in a 2-bridge knot complement, which together with the
upper and lower tunnels form the set of all known unknotting tunnels for these knots, must each be homotopic to a geodesic
of length at most 6ln(2).
First author supported by NSF Grant DMS-93028943, second author supported by the Royal Society. |
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