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Michael Abel : An introduction to Khovanov homology

Khovanov homology is a special case of a process known as categorification. The idea of categorification is to lift a known polynomial invariant of links to a homology theory whose isomorphism type is an invariant of links and whose ¡°Euler characteristic¡± is the original polynomial. In the case of Khovanov homology, this Euler characteristic is the famous Jones polynomial. After reviewing some basic knot theory and the construction of the Jones polynomial, we discuss the construction of Khovanov homology. Finally, we will discuss some topological applications of Khovanov homology.

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