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

Abstract

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.