A ug 2 00 7 THE TREE OF KNOT TUNNELS

Abstract

We present a new theory which describes the collection of all tunnels of tunnel number 1 knots in S (up to orientation-preserving equivalence in the sense of Heegaard splittings) using the disk complex of the genus-2 handlebody and associated structures. It shows that each knot tunnel is obtained from the tunnel of the trivial knot by a uniquely determined… (More)

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