ON CRITICAL HEEGAARD SPLITTINGS OF TUNNEL NUMBER TWO COMPOSITE KNOT EXTERIORS
2013 ◽
Vol 22
(11)
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pp. 1350065
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In this paper, we prove that a tunnel number two knot induces a critical Heegaard splitting in its exterior if there are two weak reducing pairs such that each weak reducing pair contains the cocore disk of each tunnel. Moreover, we prove that a connected sum of two 2-bridge knots or more generally that of two (1,1)-knots always contains a critical Heegaard splitting in its exterior as the examples of the main theorem.
2018 ◽
Vol 27
(09)
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pp. 1842003
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2012 ◽
Vol 21
(08)
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pp. 1250078
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1983 ◽
Vol 6
(3)
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pp. 511-519
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2019 ◽
Vol 28
(09)
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pp. 1950059
2013 ◽
Vol 22
(05)
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pp. 1350018
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2015 ◽
Vol 24
(02)
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pp. 1550013
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1997 ◽
pp. 1-18
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2010 ◽
Vol 149
(1)
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pp. 115-125
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