A lower bound on tunnel number degeneration
Abstract
We prove a theorem which bounds Heegaard genus from below under special kinds of toroidal amalgamations of $3$manifolds. As a consequence, we conclude $t(K_1\# K_2)\geq \max\{t(K_1),t(K_2)\}$ for any pair of knots $K_1,K_2\subset S^3$, where $t(K)$ denotes the tunnel number of $K$.
 Publication:

arXiv eprints
 Pub Date:
 July 2014
 arXiv:
 arXiv:1407.3554
 Bibcode:
 2014arXiv1407.3554S
 Keywords:

 Mathematics  Geometric Topology
 EPrint:
 22 pages, 6 figures