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ON CRITICAL HEEGAARD SPLITTINGS OF TUNNEL NUMBER TWO COMPOSITE KNOT EXTERIORS
https://doi.org/10.1142/S021821651350065XCited by:7 (Source: Crossref)
Abstract
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.
Keywords:
AMSC: 57M50, 57M25
