A recursive formula for the Khovanov cohomology of a family of 3-stranded pretzel knots.

摘要

After reviewing the process of associating graded cohomology groups (Khovanov cohomology) to a knot, we prove two lemmas that reduce the computational complexity of calculating the Khovanov cohomology. We then prove a recursive formula for the class of three-stranded pretzel knots P--( --n, --m, m), where n and m are odd. This result shows that the rank of the Khovanov cohomology of P--(--n, --m, m) is an invariant of n.