Alternating link and its generalization

Abstract

The alternating links give a classical class of links. They play an important role in Knot Theory. Ozsváth and Szabó introduced a quasi-alternating link which is a generalization of an alternating link. In this paper we review some results of alternating links and quasi-alternating links on the Jones polynomial and the Khovanov homology. Moreover, we introduce a long pass link. Several problems worthy of further study are provided.

Graphical abstract

Keywords

Alternating links / quasi-alternating links / pass replacement / Jones polynomial / Khovanov homology

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