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

Pajitnov, Andrei

doi:10.2140/agt.2010.10.627

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

Andrei Pajitnov

Algebraic & Geometric Topology 10 (2010) 627–635

DOI: 10.2140/agt.2010.10.627

Abstract

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

Keywords

tunnel number, Morse–Novikov number, Alexander polynomial

Mathematical Subject Classification 2000

Primary: 57M25, 57M27, 57R35, 57R70

Secondary: 57R19, 57R45

References

Publication

Received: 19 October 2009

Accepted: 5 January 2010

Published: 13 March 2010

Authors

Andrei Pajitnov
Laboratoire Mathématiques Jean Leray UMR 6629 Université de Nantes Faculté des Sciences 2, rue de la Houssinière 44072 Nantes Cedex France
http://www.math.sciences.univ-nantes.fr/~pajitnov/

Volume 10, issue 2 (2010)