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Characterization of Positive Links and the s-invariant for Links

Published online by Cambridge University Press:  20 November 2018

Tetsuya Abe  and
Keiji Tagami
Tetsuya Abe
Affiliation:
Osaka City University Advanced Mathematical Institute, 3-3-138 Sugimoto, Sumiyoshi-ku Osaka 558-8585, Japan e-mail: tabe@sci.osaka-cu.ac.jp
Keiji Tagami
Affiliation:
Department of Mathematics, Faculty of Science and Technology, Tokyo University of Science, Noda, Chiba, 378-8510, Japan e-mail: tagami_keiji@ma.noda.tus.ac.jp
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Abstract

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We characterize positive links in terms of strong quasipositivity, homogeneity, and thevalue of Rasmussen and Beliakova-Wehrli's $s$ -invariant. We also study almost positive links, and inparticular, determine the $s$ -invariants of almost positive links. This result suggests that all almostpositive links might be strongly quasipositive. On the other hand, it implies that almost positivelinks are never homogeneous links.

Keywords

57M2557M27(almost) positive linkhomogeneous link(strongly) quasipositive links-invariant

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 69 , Issue 6 , 01 December 2017 , pp. 1201 - 1218
Copyright
Copyright © Canadian Mathematical Society 2016

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