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 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.

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/