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Genus two Heegaard splittings of exteriors of 1-genus 1-bridge knots

Authors
  • Goda, Hiroshi
  • Hayashi, Chuichiro
Type
Preprint
Publication Date
Sep 10, 2010
Submission Date
Sep 10, 2010
Source
arXiv
License
Yellow
External links

Abstract

A knot K in a closed connected orientable 3-manifold M is called a 1-genus 1-bridge knot if (M,K) has a splitting into two pairs of a solid torus V_i (i=1,2) and a boundary parallel arc in it. The splitting induces a genus two Heegaard splitting of the exterior of K naturally, i.e., K has an unknotting tunnel. However the converse is not true in general. Then we study such general case in this paper. One of the conclusions is that the unknotting tunnel may be levelled with the torus \partial V_1=\partial V_2.

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