Characterization of positive links and the $s$-invariant for links
Abstract
We characterize positive links in terms of strong quasipositivity, homogeneity and the value of Rasmussen, Beliakova and 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.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2014
- DOI:
- 10.48550/arXiv.1405.4061
- arXiv:
- arXiv:1405.4061
- Bibcode:
- 2014arXiv1405.4061A
- Keywords:
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- Mathematics - Geometric Topology
- E-Print:
- 18 pages, 10 figures, v5:the statements of Corollary 1.7 and Corollary 7.4 were corrected, Question 10.5 and two references were added, v6:this is the published version, survey parts are deleted