Additive tunnel number and primitive elements

Details Additive tunnel number and primitive elements Additive tunnel number and primitive elements

1999-06-10

arxiv.org/abs/math/9906061v1

Mathematics

Geometric Topology

20 pages, 11 figures

Scientific paper

It is proven here that if the connected sum of two tunnel number one knots in
the 3-sphere is a tunnel number two knot, then at least one of the summand
knots has a genus two Heegaard splitting with a meridian as a primitive
element. Hence this is a necessary and sufficient condition for tunnel number
one knots to have additive tunnel number.

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