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 $t(K_1\#K_2)\ge \max \{t(K_1),t(K_2)\}$ for any pair of knots $K_1,K_2\subset S^3$, where $t(K)$ denotes the tunnel number of $K$.

22 pages, 6 figures

References in corpus (1)

• Tunnel number degeneration under the connected sum of prime knots

Cited by in corpus (1)

• Tunnel number and bridge number of composite genus 2 spatial graphs