Superbridge index of composite knots

Details Superbridge index of composite knots Superbridge index of composite knots

2000-01-15

arxiv.org/abs/math/0001090v2

Journal of Knot Theory and its Ramifications, vol.9, no.5 (2000) 669-682

Mathematics

Geometric Topology

14 pages, 5 figures, 1 table

Scientific paper

An upper bound of the superbridge index of the connected sum of two knots is given in terms of the braid index of the summands. Using this upper bound and minimal polygonal presentations, we give an upper bound in terms of the superbridge index and the bridge index of the summands when they are torus knots. In contrast to the fact that the difference between the sum of bridge indices of two knots and the bridge index of their connected sum is always one, the corresponding difference for the superbridge index can be arbitrarily large.

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