Khovanov Homology: A Categorification of the Jones Polynomial
摘要
The theory of invariants of knots and links was revolutionized with the discovery of the Jones polynomial in 1984. At the end of the twentieth century, Mikhail Khovanov announced a novel construction of a new and very powerful link invariant: a homology theory categorifying the Jones polynomial, containing more information, and having a richer algebraic structure. One of the spectacular applications of Khovanov homology is that it detects the unknot. In this lecture, we present an elementary exposition of Khovanov homology following the construction by Oleg Viro.