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# Characterization of Positive Links and the $s$-invariant for Links

Published:2016-11-29
Printed: Dec 2017
• Tetsuya Abe,
Osaka City University Advanced Mathematical Institute, 3-3-138 Sugimoto, Sumiyoshi-ku Osaka 558-8585 Japan
• Keiji Tagami,
Department of Mathematics, Faculty of Science and Technology, Tokyo University of Science, Noda, Chiba, 278-8510, Japan
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## Abstract

We characterize positive links in terms of strong quasipositivity, homogeneity and the value of Rasmussen and Beliakova-Wehrli's $s$-invariant. We also study almost positive links, in particular, determine the $s$-invariants of almost positive links. This result suggests that all almost positive links might be strongly quasipositive. On the other hand, it implies that almost positive links are never homogeneous links.
 Keywords: knot, $s$-invariant, positive link, almost positive link
 MSC Classifications: 57M25 - Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M27 - Invariants of knots and 3-manifolds

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