We define the meridional destabilizing number of a knot. This together with Heegaard genus (or tunnel number) gives a binary complexity of knots. We study its behavior under connected sum of tunnel number one knots.
"Meridional destabilizing number of knots." Algebr. Geom. Topol. 11 (2) 1205 - 1242, 2011. https://doi.org/10.2140/agt.2011.11.1205