On critical Heegaard splittings of tunnel number two composite knot exteriors

Jungsoo Kim

doi:10.1142/s021821651350065x

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arXiv · 1210.3174

On critical Heegaard splittings of tunnel number two composite knot exteriors

Jungsoo Kim

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Abstract

In this article, 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 can induce a critical Heegaard splitting in its exterior as the examples of the main theorem. Finally, we give an equivalent condition for a weak reducing pair to be determined by a compressing disk uniquely when the manifold is closed, irreducible and the Heegaard splitting is of genus three and unstabilized.

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BibTeX RIS

Jungsoo Kim. 2012-10-15. On critical Heegaard splittings of tunnel number two composite knot exteriors. https://doi.org/10.1142/s021821651350065x

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