  A second part of detailed elementary introduction into Khovanov homologies.
This part is devoted to reduced Jones superpolynomials. The story is still
about a hypercube of resolutions of a link diagram. Each resolution is a
collection of non-intersecting cycles, and one associates a 2-dimensional
vector space with each cycle. Reduced superpolynomial arises when for all
cycles, containing a "marked" edge of the link diagram, the vector space is
reduced to 1-dimensional. The rest remains the same. Edges of the hypercube are
associated with cut-and-join operators, acting on the cycles. Superpartners of
these operators can be combined into differentials of a complex, and
superpolynomial is the Poincare polynomial of this complex. HOMFLY polynomials
are practically the same in reduced and unreduced case, but superpolynomials
are essentially different, already in the simplest examples of trefoil and
figure-eight knot.
