Additive tunnel number and primitive elements
Geometric Topology
2009-09-25 v1
Abstract
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.
Keywords
Cite
@article{arxiv.math/9906061,
title = {Additive tunnel number and primitive elements},
author = {Yoav Moriah},
journal= {arXiv preprint arXiv:math/9906061},
year = {2009}
}
Comments
20 pages, 11 figures