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High distance knots

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.

5 nodes4 linksoverview previewHigh distance knots
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5 nodes4 links
High distance knots5 visible / 5 total nodes / 7 links
Co-authorshipCo-authorshipCo-authorshipAuthorshipAuthorshipAuthorshipTopic signalWHigh distance knotspreprint / 2007AYair MinskyResearcherAYoav MoriahResearcherASaul SchleimerResearcherTmath.GT2393 works
PaperSignal 104 links

High distance knots

preprint / 2007

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