Destabilizing Heegaard splittings of knot exteriors

作者：Kobayashi Tsuyoshi^*; Saito Toshio

来源：Topology and Its Applications, 2010, 157(1): 202-212.

DOI：10.1016/j.topol.2009.04.059

• Heegaard splitting
• Unknotting tunnel system
• Destabilization

We give a necessary and sufficient condition for Heegaard splittings of knot exteriors to admit destabilizations. As an application. we show the following: let K-1 and K-2 be a pair of knots which is introduced by Morimoto as an example giving degeneration of tunnel number under connected sum. The Heegaard splitting of the exterior of K-1 # K-2 derived from certain minimal unknotting tunnel systems of K-1 and K-2 is stabilized.

• 出版日期2010-1-1