arXiv 1407.35542014-07-14math.GT

A lower bound on tunnel number degeneration

Trent Schirmer

备注：: 22 pages, 6 figures
发表信息：: Algebr. Geom. Topol. 16 (2016) 1279-1308
DOI：: 10.2140/agt.2016.16.1279

英文摘要：

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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