A Formula for Khovanov Type Link Homology of Pretzel Knots

Abstract

Khovanov type homology is a generalization of Khovanov homology. The main result of this paper is to give a recursive formula for Khovanov type homology of pretzel knots $P(−n, −m, m)$. The computations reveal that the rank of the homology of pretzel knots is an invariant of $n$. The proof is based on a "shortcut" and two lemmas that recursively reduce the computational complexity of Khovanov type homology.