#### Volume 10, issue 2 (2010)

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On the tunnel number and the Morse–Novikov number of knots

### Andrei Pajitnov

Algebraic & Geometric Topology 10 (2010) 627–635
##### Abstract

Let $L$ be a link in ${S}^{3}$; denote by $\mathsc{ℳ}\mathsc{N}\left(L\right)$ the Morse–Novikov number of $L$ and by $t\left(L\right)$ the tunnel number of $L$. We prove that $\mathsc{ℳ}\mathsc{N}\left(L\right)\le 2t\left(L\right)$ and deduce several corollaries.

##### Keywords
tunnel number, Morse–Novikov number, Alexander polynomial
##### Mathematical Subject Classification 2000
Primary: 57M25, 57M27, 57R35, 57R70
Secondary: 57R19, 57R45