Algebraic & Geometric Topology

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

Andrei Pajitnov

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Let L be a link in S3; denote by N(L) the Morse–Novikov number of L and by t(L) the tunnel number of L. We prove that N(L)2t(L) and deduce several corollaries.

Article information

Algebr. Geom. Topol., Volume 10, Number 2 (2010), 627-635.

Received: 19 October 2009
Accepted: 5 January 2010
First available in Project Euclid: 19 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M27: Invariants of knots and 3-manifolds 57R35: Differentiable mappings 57R70: Critical points and critical submanifolds
Secondary: 57R19: Algebraic topology on manifolds 57R45: Singularities of differentiable mappings

tunnel number Morse–Novikov number Alexander polynomial


Pajitnov, Andrei. On the tunnel number and the Morse–Novikov number of knots. Algebr. Geom. Topol. 10 (2010), no. 2, 627--635. doi:10.2140/agt.2010.10.627.

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