| We present the construction of (KR) Khovanov-Rozansky sl( n) link homology which is a link invariant in the form of a doubly graded C -space. Invariant's Euler characteristic relative to one grading equals the n-Jones polynomial. We extend Lee's result on Khovanov link homology (n = 2) to the general case of KR link homology: we exhibit a spectral sequence which starts with the KR link homology and converges to the easily manageable deformed KR link homology. The deformed KR link homology is explicitly calculated: as a C -space it depends only on the number of components of the link and their linking numbers; in the case of a knot K its grading is entirely determined by a single integer sn( K) which is a link invariant. We study the behavior of KR link homology and its deformed variant under the operation of replacing the link L with its mirror -L. We show that, relative to its double grading, the (i, j) summand of KR link homology of L is dual to the (-i,-j) summand of KR homology of -L for all i, j ∈ N . Similarly, in the deformed case we show that sn( K) = -sn(-K). |
