Khovanov Homology
In the field of knot theory there are many different types of knot invariants used to help distinguish knots from one another. In the year 2000, Mikhail Khovanov published A categorification of the Jones polynomial. Within this paper it is proven that through the use of the “Khovanov bracket” (as defined in the paper), one may ascertain the graded Euler characteristic of a knot. Furthermore, if one is to apply the correct renormilization to the Khovanov bracket a polynomial invariant will be attained, namely the “Khovanov homology”. Not included in the paper is a proof of invariance of the Jones polynomial with respect to the state-sum expressions within the construction of the “Khovanov Bracket”. At this point is in the interest of Jose Chavez to come up with such a proof in order that he will be able to better understand Khovanov Homology as a whole and thus be able to contribute more meaningful work in the future.