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.
Saito, Toshio  1
@article{10_2140_agt_2011_11_1205,
author = {Saito, Toshio},
title = {Meridional destabilizing number of knots},
journal = {Algebraic and Geometric Topology},
pages = {1205--1242},
year = {2011},
volume = {11},
number = {2},
doi = {10.2140/agt.2011.11.1205},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2011.11.1205/}
}
Saito, Toshio. Meridional destabilizing number of knots. Algebraic and Geometric Topology, Tome 11 (2011) no. 2, pp. 1205-1242. doi: 10.2140/agt.2011.11.1205
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