A lower bound on tunnel number degeneration

@inproceedings{Schirmer2016ALB,
  title={A lower bound on tunnel number degeneration},
  author={Trent Schirmer},
  year={2016}
}
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 $K$. 
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