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Destabilizing Heegaard splittings of knot exteriors |
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| Authors: | Tsuyoshi Kobayashi Toshio Saito |
| Institution: | aGraduate School of Humanities and Sciences, Nara Women's University, Kitauoya Nishimachi, Nara 630-8506, Japan;bDepartment of Mathematics, South Hall, Room 6607, University of California, Santa Barbara, CA 93106, USA |
| Abstract: | We give a necessary and sufficient condition for Heegaard splittings of knot exteriors to admit destabilizations. As an application, we show the following: let K1 and K2 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 K1#K2 derived from certain minimal unknotting tunnel systems of K1 and K2 is stabilized. |
| Keywords: | Heegaard splitting Unknotting tunnel system Destabilization |
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