Year: 1999
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Moriah, Yoav
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1609828241