High distance knots

Details High distance knots High distance knots

2006-07-11

arxiv.org/abs/math/0607265v3

Mathematics

Geometric Topology

13 pages, 3 figures. Added reference

Scientific paper

We construct knots in S^3 with Heegaard splittings of arbitrarily high
distance, in any genus. As an application, for any positive integers t and b we
find a tunnel number t knot in the three-sphere which has no
(t,b)-decomposition.

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