Unknotting tunnels in two-bridge knot and link complements

被引:22
作者
Adams, CC [1 ]
Reid, AW [1 ]
机构
[1] UNIV TEXAS,DEPT MATH,AUSTIN,TX 78712
关键词
D O I
10.1007/BF02566439
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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).
引用
收藏
页码:617 / 627
页数:11
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